diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index e9996dcf8bc6a..83084f78ccc3b 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -82,6 +82,7 @@ Other enhancements
 - :meth:`Series.map` can now accept kwargs to pass on to func (:issue:`59814`)
 - :meth:`Series.map` now accepts an ``engine`` parameter to allow execution with a third-party execution engine (:issue:`61125`)
 - :meth:`Series.rank` and :meth:`DataFrame.rank` with numpy-nullable dtypes preserve ``NA`` values and return ``UInt64`` dtype where appropriate instead of casting ``NA`` to ``NaN`` with ``float64`` dtype (:issue:`62043`)
+- :meth:`Series.round` raising ``TypeError`` for ``object`` dtype with ``pd.NA``. The result now coerces to nullable ``Float64`` and rounds as expected (:issue:`61712`).
 - :meth:`Series.str.get_dummies` now accepts a  ``dtype`` parameter to specify the dtype of the resulting DataFrame (:issue:`47872`)
 - :meth:`pandas.concat` will raise a ``ValueError`` when ``ignore_index=True`` and ``keys`` is not ``None`` (:issue:`59274`)
 - :py:class:`frozenset` elements in pandas objects are now natively printed (:issue:`60690`)
@@ -97,7 +98,7 @@ Other enhancements
 - Support passing a :class:`Iterable[Hashable]` input to :meth:`DataFrame.drop_duplicates` (:issue:`59237`)
 - Support reading Stata 102-format (Stata 1) dta files (:issue:`58978`)
 - Support reading Stata 110-format (Stata 7) dta files (:issue:`47176`)
--
+
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_300.notable_bug_fixes:
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 6ae03f2464f76..a6996867fb541 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -2516,6 +2516,20 @@ def round(self, decimals: int = 0, *args, **kwargs) -> Series:
         """
         nv.validate_round(args, kwargs)
         if self.dtype == "object":
+            # If the object-dtype Series contains pd.NA and is otherwise numeric,
+            # cast to nullable Float64 and round. Otherwise, fall back to the
+            # existing implementation to preserve prior behavior (incl. errors).
+            has_pd_na = self.isna().any()
+            if has_pd_na:
+                try:
+                    converted = self.astype("Float64")
+                except Exception as err:
+                    raise TypeError(
+                        "Expected numeric dtype, got object instead."
+                    ) from err
+                else:
+                    return converted.round(decimals)
+
             raise TypeError("Expected numeric dtype, got object instead.")
         new_mgr = self._mgr.round(decimals=decimals)
         return self._constructor_from_mgr(new_mgr, axes=new_mgr.axes).__finalize__(
diff --git a/pandas/tests/series/methods/test_round.py b/pandas/tests/series/methods/test_round.py
index a78f77e990ae1..0779a00b2d79d 100644
--- a/pandas/tests/series/methods/test_round.py
+++ b/pandas/tests/series/methods/test_round.py
@@ -79,3 +79,10 @@ def test_round_dtype_object(self):
         msg = "Expected numeric dtype, got object instead."
         with pytest.raises(TypeError, match=msg):
             ser.round()
+
+    def test_round_with_pd_na(self):
+        # GH61712
+        s = Series([0.5, pd.NA], dtype="object")
+        result = s.round(0)
+        expected = Series([0.0, pd.NA], dtype="Float64")
+        tm.assert_series_equal(result, expected)