diff --git a/docs/src/apireference.md b/docs/src/apireference.md
index 90275a08de..67998d50e2 100644
--- a/docs/src/apireference.md
+++ b/docs/src/apireference.md
@@ -707,6 +707,7 @@ Bridges.Constraint.ScalarFunctionizeBridge
 Bridges.Constraint.VectorFunctionizeBridge
 Bridges.Constraint.SplitIntervalBridge
 Bridges.Constraint.RSOCBridge
+Bridges.Constraint.SOCRBridge
 Bridges.Constraint.QuadtoSOCBridge
 Bridges.Constraint.GeoMeanBridge
 Bridges.Constraint.SquareBridge
diff --git a/src/Bridges/Constraint/Constraint.jl b/src/Bridges/Constraint/Constraint.jl
index 5041121052..6197a1e503 100644
--- a/src/Bridges/Constraint/Constraint.jl
+++ b/src/Bridges/Constraint/Constraint.jl
@@ -36,6 +36,8 @@ include("interval.jl")
 const SplitInterval{T, OT<:MOI.ModelLike} = SingleBridgeOptimizer{SplitIntervalBridge{T}, OT}
 include("rsoc.jl")
 const RSOC{T, OT<:MOI.ModelLike} = SingleBridgeOptimizer{RSOCBridge{T}, OT}
+include("socr.jl")
+const SOCR{T, OT<:MOI.ModelLike} = SingleBridgeOptimizer{SOCRBridge{T}, OT}
 include("quad_to_soc.jl")
 const QuadtoSOC{T, OT<:MOI.ModelLike} = SingleBridgeOptimizer{QuadtoSOCBridge{T}, OT}
 include("geomean.jl")
@@ -74,8 +76,10 @@ function add_all_bridges(bridged_model, T::Type)
     MOIB.add_bridge(bridged_model, LogDetBridge{T})
     MOIB.add_bridge(bridged_model, RootDetBridge{T})
     MOIB.add_bridge(bridged_model, RSOCBridge{T})
+    MOIB.add_bridge(bridged_model, SOCRBridge{T})
+    # We do not add `SOCtoPSDBridge` as transforming the `SOC` to `RSOC` and
+    # then to `PSD` produces a smaller SDP constraint.
     MOIB.add_bridge(bridged_model, RSOCtoPSDBridge{T})
-    MOIB.add_bridge(bridged_model, SOCtoPSDBridge{T})
     MOIB.add_bridge(bridged_model, IndicatorActiveOnFalseBridge{T})
     return
 end
diff --git a/src/Bridges/Constraint/rsoc.jl b/src/Bridges/Constraint/rsoc.jl
index adf063d4b7..7b75878fce 100644
--- a/src/Bridges/Constraint/rsoc.jl
+++ b/src/Bridges/Constraint/rsoc.jl
@@ -58,7 +58,7 @@ function concrete_bridge_type(::Type{<:RSOCBridge{T}},
     Y = MOIU.promote_operation(-, T, S, S)
     Z = MOIU.promote_operation(+, T, S, S)
     F = MOIU.promote_operation(vcat, T, Z, Y, G)
-    RSOCBridge{T, F, G}
+    return RSOCBridge{T, F, G}
 end
 
 # Attributes, Bridge acting as a model
@@ -72,8 +72,8 @@ function MOI.get(b::RSOCBridge{T, F},
 end
 
 # References
-function MOI.delete(model::MOI.ModelLike, c::RSOCBridge)
-    MOI.delete(model, c.soc)
+function MOI.delete(model::MOI.ModelLike, bridge::RSOCBridge)
+    MOI.delete(model, bridge.soc)
 end
 
 # Attributes, Bridge acting as a constraint
@@ -88,12 +88,22 @@ function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintSet, bridge::RSOCBrid
     return MOI.RotatedSecondOrderCone(MOI.dimension(set))
 end
 # As the linear transformation is a symmetric involution,
-# the constraint primal and dual both need to be processed by reapplying the same transformation
-function _get(model, attr::Union{MOI.ConstraintPrimal, MOI.ConstraintDual}, c::RSOCBridge)
-    x = MOI.get(model, attr, c.soc)
+# the constraint primal and dual both need to be processed by reapplying the
+# same transformation
+function rotate_result(model,
+                       attr::Union{MOI.ConstraintPrimal, MOI.ConstraintDual},
+                       ci::MOI.ConstraintIndex)
+    x = MOI.get(model, attr, ci)
     s2 = √2
-    [x[1]/s2+x[2]/s2; x[1]/s2-x[2]/s2; x[3:end]]
+    return [x[1]/s2 + x[2]/s2; x[1]/s2 - x[2]/s2; x[3:end]]
+end
+# Need to define both `get` methods and redirect to `rotate_result` to avoid
+# ambiguity in dispatch
+function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintPrimal,
+                 bridge::RSOCBridge)
+    return rotate_result(model, attr, bridge.soc)
+end
+function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintDual,
+                 bridge::RSOCBridge)
+    return rotate_result(model, attr, bridge.soc)
 end
-# Need to define both `get` methods and redirect to `_get` to avoid ambiguity in dispatch
-MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintPrimal, c::RSOCBridge) = _get(model, attr, c)
-MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintDual, c::RSOCBridge) = _get(model, attr, c)
diff --git a/src/Bridges/Constraint/soc_to_psd.jl b/src/Bridges/Constraint/soc_to_psd.jl
index 85257f692a..f9973fff5a 100644
--- a/src/Bridges/Constraint/soc_to_psd.jl
+++ b/src/Bridges/Constraint/soc_to_psd.jl
@@ -50,6 +50,10 @@ which is equivalent to
   t^2 & > x^\\top x
 \\end{align*}
 ```
+This bridge is not added by default by [`full_bridge_optimizer`](@ref) as
+bridging second order cone constraints to semidefinite constraints can be
+achieved by the [`SOCRBridge`](@ref) followed by the [`RSOCtoPSDBridge`](@ref)
+while creating a smaller semidefinite constraint.
 """
 struct SOCtoPSDBridge{T} <: AbstractBridge
     dim::Int
diff --git a/src/Bridges/Constraint/socr.jl b/src/Bridges/Constraint/socr.jl
new file mode 100644
index 0000000000..98bbb0b91a
--- /dev/null
+++ b/src/Bridges/Constraint/socr.jl
@@ -0,0 +1,74 @@
+"""
+    SOCRBridge{T, F, G}
+
+The `SecondOrderCone` is `RotatedSecondOrderCone`. We simply do the inverse
+transformation of [`RSOCBridge`](@ref). In fact, as the transformation is an
+involution, we do the same transformation.
+
+"""
+struct SOCRBridge{T, F, G} <: AbstractBridge
+    rsoc::CI{F, MOI.RotatedSecondOrderCone}
+end
+function bridge_constraint(::Type{SOCRBridge{T, F, G}}, model,
+                           f::MOI.AbstractVectorFunction,
+                           s::MOI.SecondOrderCone) where {T, F, G}
+    soc = MOI.add_constraint(model, rotate_function(f, T),
+                             MOI.RotatedSecondOrderCone(MOI.dimension(s)))
+    return SOCRBridge{T, F, G}(soc)
+end
+
+function MOI.supports_constraint(::Type{SOCRBridge{T}},
+                                ::Type{<:MOI.AbstractVectorFunction},
+                                ::Type{MOI.SecondOrderCone}) where T
+    return true
+end
+MOIB.added_constrained_variable_types(::Type{<:SOCRBridge}) = Tuple{DataType}[]
+function MOIB.added_constraint_types(::Type{<:SOCRBridge{T, F}}) where {T, F}
+    return [(F, MOI.RotatedSecondOrderCone)]
+end
+function concrete_bridge_type(::Type{<:SOCRBridge{T}},
+                              G::Type{<:MOI.AbstractVectorFunction},
+                              ::Type{MOI.SecondOrderCone}) where T
+    S = MOIU.promote_operation(/, T, MOIU.scalar_type(G), T)
+    Y = MOIU.promote_operation(-, T, S, S)
+    Z = MOIU.promote_operation(+, T, S, S)
+    F = MOIU.promote_operation(vcat, T, Z, Y, G)
+    return SOCRBridge{T, F, G}
+end
+
+# Attributes, Bridge acting as an model
+function MOI.get(b::SOCRBridge{T, F},
+                 ::MOI.NumberOfConstraints{F, MOI.RotatedSecondOrderCone}) where {T, F}
+    return 1
+end
+function MOI.get(b::SOCRBridge{T, F},
+                 ::MOI.ListOfConstraintIndices{F, MOI.RotatedSecondOrderCone}) where {T, F}
+    return [b.rsoc]
+end
+
+# References
+function MOI.delete(model::MOI.ModelLike, bridge::SOCRBridge)
+    MOI.delete(model, bridge.rsoc)
+end
+
+# Attributes, Bridge acting as a constraint
+function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintFunction,
+                 bridge::SOCRBridge{T, F, G}) where {T, F, G}
+    # As it is an involution, we can just reapply the same transformation
+    func = MOI.get(model, attr, bridge.rsoc)
+    return MOIU.convert_approx(G, rotate_function(func, T))
+end
+function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintSet, bridge::SOCRBridge)
+    set = MOI.get(model, attr, bridge.rsoc)
+    return MOI.SecondOrderCone(MOI.dimension(set))
+end
+# As the linear transformation is a symmetric involution,
+# the constraint primal and dual both need to be processed by reapplying the same transformation
+function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintPrimal,
+                 bridge::SOCRBridge)
+    return rotate_result(model, attr, bridge.rsoc)
+end
+function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintDual,
+                 bridge::SOCRBridge)
+    return rotate_result(model, attr, bridge.rsoc)
+end
diff --git a/test/Bridges/Constraint/Constraint.jl b/test/Bridges/Constraint/Constraint.jl
index dbce4c1017..af0269353e 100644
--- a/test/Bridges/Constraint/Constraint.jl
+++ b/test/Bridges/Constraint/Constraint.jl
@@ -9,6 +9,7 @@ include("slack.jl")
 include("functionize.jl")
 include("interval.jl")
 include("rsoc.jl")
+include("socr.jl")
 include("quad_to_soc.jl")
 include("geomean.jl")
 include("square.jl")
diff --git a/test/Bridges/Constraint/socr.jl b/test/Bridges/Constraint/socr.jl
new file mode 100644
index 0000000000..446d3fb6f8
--- /dev/null
+++ b/test/Bridges/Constraint/socr.jl
@@ -0,0 +1,39 @@
+using Test
+
+using MathOptInterface
+const MOI = MathOptInterface
+const MOIT = MathOptInterface.Test
+const MOIU = MathOptInterface.Utilities
+const MOIB = MathOptInterface.Bridges
+
+include("utilities.jl")
+
+mock = MOIU.MockOptimizer(MOIU.Model{Float64}())
+config = MOIT.TestConfig()
+
+@testset "RSOC" begin
+    bridged_mock = MOIB.SOCR{Float64}(mock)
+
+    MOIT.basic_constraint_tests(
+        bridged_mock, config,
+        include = [(F, S)
+                   for F in [MOI.VectorOfVariables, MOI.VectorAffineFunction{Float64},
+                             MOI.VectorQuadraticFunction{Float64}]
+                   for S in [MOI.SecondOrderCone]])
+
+    mock.optimize! = (mock::MOIU.MockOptimizer) -> MOIU.mock_optimize!(mock, [1.0, 1/√2, 1/√2],
+                          (MOI.VectorAffineFunction{Float64}, MOI.RotatedSecondOrderCone) => [[1 - 1/√2, 1 + 1/√2, -1]],
+                          (MOI.VectorAffineFunction{Float64}, MOI.Zeros)           => [[-√2]])
+    MOIT.soc1vtest(bridged_mock, config)
+    mock.optimize! = (mock::MOIU.MockOptimizer) -> MOIU.mock_optimize!(mock, [1.0, 1/√2, 1/√2],
+                          (MOI.VectorAffineFunction{Float64}, MOI.RotatedSecondOrderCone) => [[1 - 1/√2, 1 + 1/√2, -1]],
+                          (MOI.VectorAffineFunction{Float64}, MOI.Zeros)           => [[-√2]])
+    MOIT.soc1ftest(bridged_mock, config)
+    ci = first(MOI.get(
+        bridged_mock,
+        MOI.ListOfConstraintIndices{MOI.VectorAffineFunction{Float64},
+                                    MOI.SecondOrderCone}()))
+    test_delete_bridge(bridged_mock, ci, 3,
+                       ((MOI.VectorAffineFunction{Float64},
+                         MOI.RotatedSecondOrderCone, 0),))
+end