diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index 1bbec97756e79..6250c298f291f 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -853,6 +853,45 @@ def _concat_same_type(
         arr = pa.chunked_array(chunks)
         return cls(arr)
 
+    def _accumulate(
+        self, name: str, *, skipna: bool = True, **kwargs
+    ) -> ArrowExtensionArray | ExtensionArray:
+        """
+        Return an ExtensionArray performing an accumulation operation.
+
+        The underlying data type might change.
+
+        Parameters
+        ----------
+        name : str
+            Name of the function, supported values are:
+            - cummin
+            - cummax
+            - cumsum
+            - cumprod
+        skipna : bool, default True
+            If True, skip NA values.
+        **kwargs
+            Additional keyword arguments passed to the accumulation function.
+            Currently, there is no supported kwarg.
+
+        Returns
+        -------
+        array
+
+        Raises
+        ------
+        NotImplementedError : subclass does not define accumulations
+        """
+        pyarrow_name = {
+            "cumsum": "cumulative_sum_checked",
+        }.get(name, name)
+        pyarrow_meth = getattr(pc, pyarrow_name, None)
+        if pyarrow_meth is None:
+            return super()._accumulate(name, skipna=skipna, **kwargs)
+        result = pyarrow_meth(self._data, skip_nulls=skipna, **kwargs)
+        return type(self)(result)
+
     def _reduce(self, name: str, *, skipna: bool = True, **kwargs):
         """
         Return a scalar result of performing the reduction operation.
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index f93cf3d6bc138..9b42b86efd0d0 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -343,6 +343,54 @@ def test_getitem_scalar(self, data):
         super().test_getitem_scalar(data)
 
 
+class TestBaseAccumulateTests(base.BaseAccumulateTests):
+    def check_accumulate(self, s, op_name, skipna):
+        result = getattr(s, op_name)(skipna=skipna).astype("Float64")
+        expected = getattr(s.astype("Float64"), op_name)(skipna=skipna)
+        self.assert_series_equal(result, expected, check_dtype=False)
+
+    @pytest.mark.parametrize("skipna", [True, False])
+    def test_accumulate_series_raises(
+        self, data, all_numeric_accumulations, skipna, request
+    ):
+        pa_type = data.dtype.pyarrow_dtype
+        if (
+            (pa.types.is_integer(pa_type) or pa.types.is_floating(pa_type))
+            and all_numeric_accumulations == "cumsum"
+            and not pa_version_under9p0
+        ):
+            request.node.add_marker(
+                pytest.mark.xfail(
+                    reason=f"{all_numeric_accumulations} implemented for {pa_type}"
+                )
+            )
+        op_name = all_numeric_accumulations
+        ser = pd.Series(data)
+
+        with pytest.raises(NotImplementedError):
+            getattr(ser, op_name)(skipna=skipna)
+
+    @pytest.mark.parametrize("skipna", [True, False])
+    def test_accumulate_series(self, data, all_numeric_accumulations, skipna, request):
+        pa_type = data.dtype.pyarrow_dtype
+        if all_numeric_accumulations != "cumsum" or pa_version_under9p0:
+            request.node.add_marker(
+                pytest.mark.xfail(
+                    reason=f"{all_numeric_accumulations} not implemented",
+                    raises=NotImplementedError,
+                )
+            )
+        elif not (pa.types.is_integer(pa_type) or pa.types.is_floating(pa_type)):
+            request.node.add_marker(
+                pytest.mark.xfail(
+                    reason=f"{all_numeric_accumulations} not implemented for {pa_type}"
+                )
+            )
+        op_name = all_numeric_accumulations
+        ser = pd.Series(data)
+        self.check_accumulate(ser, op_name, skipna)
+
+
 class TestBaseNumericReduce(base.BaseNumericReduceTests):
     def check_reduce(self, ser, op_name, skipna):
         pa_dtype = ser.dtype.pyarrow_dtype