diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index d6fd017ff0897..ffacd82b35056 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -54,6 +54,7 @@ Other enhancements
 - Add support for dict-like names in :class:`MultiIndex.set_names` and :class:`MultiIndex.rename` (:issue:`20421`)
 - :func:`pandas.read_excel` can now auto detect .xlsb files (:issue:`35416`)
 - :meth:`.Rolling.sum`, :meth:`.Expanding.sum`, :meth:`.Rolling.mean`, :meth:`.Expanding.mean`, :meth:`.Rolling.median`, :meth:`.Expanding.median`, :meth:`.Rolling.max`, :meth:`.Expanding.max`, :meth:`.Rolling.min`, and :meth:`.Expanding.min` now support ``Numba`` execution with the ``engine`` keyword (:issue:`38895`)
+- Added :meth:`NumericArray.round` (:issue:`38844`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/arrays/numeric.py b/pandas/core/arrays/numeric.py
index 3c115ec42f6ec..0325b008d88ee 100644
--- a/pandas/core/arrays/numeric.py
+++ b/pandas/core/arrays/numeric.py
@@ -1,10 +1,12 @@
 import datetime
-from typing import TYPE_CHECKING, Union
+from typing import TYPE_CHECKING, Callable, Union
 
 import numpy as np
 
 from pandas._libs import Timedelta, missing as libmissing
+from pandas.compat.numpy import function as nv
 from pandas.errors import AbstractMethodError
+from pandas.util._decorators import doc
 
 from pandas.core.dtypes.common import (
     is_float,
@@ -56,6 +58,32 @@ def __from_arrow__(
             return array_class._concat_same_type(results)
 
 
+_round_doc = """
+Round each value in NumericArray a to the given number of decimals.
+
+Parameters
+----------
+decimals : int, default 0
+    Number of decimal places to round to. If decimals is negative,
+    it specifies the number of positions to the left of the decimal point.
+*args, **kwargs
+    Additional arguments and keywords have no effect but might be
+    accepted for compatibility with NumPy.
+
+Returns
+-------
+NumericArray
+    Rounded values of the NumericArray.
+
+See Also
+--------
+numpy.around : Round values of an np.array.
+DataFrame.round : Round values of a DataFrame.
+Series.round : Round values of a Series.
+
+"""
+
+
 class NumericArray(BaseMaskedArray):
     """
     Base class for IntegerArray and FloatingArray.
@@ -130,3 +158,16 @@ def _arith_method(self, other, op):
             )
 
         return self._maybe_mask_result(result, mask, other, op_name)
+
+    def _apply(self, func: Callable, **kwargs) -> "NumericArray":
+        values = self._data[~self._mask]
+        values = np.round(values, **kwargs)
+
+        data = np.zeros(self._data.shape)
+        data[~self._mask] = values
+        return type(self)(data, self._mask)
+
+    @doc(_round_doc)
+    def round(self, decimals: int = 0, *args, **kwargs) -> "NumericArray":
+        nv.validate_round(args, kwargs)
+        return self._apply(np.round, decimals=decimals, **kwargs)
diff --git a/pandas/tests/series/methods/test_round.py b/pandas/tests/series/methods/test_round.py
index 88d5c428712dc..0f0a4e9adaa80 100644
--- a/pandas/tests/series/methods/test_round.py
+++ b/pandas/tests/series/methods/test_round.py
@@ -35,15 +35,23 @@ def test_round_numpy_with_nan(self):
         expected = Series([2.0, np.nan, 0.0])
         tm.assert_series_equal(result, expected)
 
-    def test_round_builtin(self):
-        ser = Series([1.123, 2.123, 3.123], index=range(3))
-        result = round(ser)
-        expected_rounded0 = Series([1.0, 2.0, 3.0], index=range(3))
+    def test_round_builtin(self, any_float_allowed_nullable_dtype):
+        ser = Series(
+            [1.123, 2.123, 3.123],
+            index=range(3),
+            dtype=any_float_allowed_nullable_dtype,
+        )
+        result = round(ser).astype(any_float_allowed_nullable_dtype)
+        expected_rounded0 = Series(
+            [1.0, 2.0, 3.0], index=range(3), dtype=any_float_allowed_nullable_dtype
+        )
         tm.assert_series_equal(result, expected_rounded0)
 
         decimals = 2
-        expected_rounded = Series([1.12, 2.12, 3.12], index=range(3))
-        result = round(ser, decimals)
+        expected_rounded = Series(
+            [1.12, 2.12, 3.12], index=range(3), dtype=any_float_allowed_nullable_dtype
+        )
+        result = round(ser, decimals).astype(any_float_allowed_nullable_dtype)
         tm.assert_series_equal(result, expected_rounded)
 
     @pytest.mark.parametrize("method", ["round", "floor", "ceil"])