diff --git a/cirq/ops/global_phase_op.py b/cirq/ops/global_phase_op.py
index 576300a1350..9a2802d2224 100644
--- a/cirq/ops/global_phase_op.py
+++ b/cirq/ops/global_phase_op.py
@@ -59,6 +59,14 @@ def _apply_unitary_(self, args) -> np.ndarray:
         args.target_tensor *= self.coefficient
         return args.target_tensor
 
+    def _act_on_(self, args: Any):
+        from cirq.sim import clifford
+        if isinstance(args, clifford.ActOnStabilizerCHFormArgs):
+            args.state.omega *= self.coefficient  # type: ignore
+            return True
+
+        return NotImplemented
+
     def __str__(self) -> str:
         return str(self.coefficient)
 
diff --git a/cirq/ops/global_phase_op_test.py b/cirq/ops/global_phase_op_test.py
index 12bbef97cd2..f2ae9049951 100644
--- a/cirq/ops/global_phase_op_test.py
+++ b/cirq/ops/global_phase_op_test.py
@@ -40,6 +40,14 @@ def test_protocols():
                                atol=1e-8)
 
 
+@pytest.mark.parametrize('phase', [1, 1j, -1])
+def test_act_on(phase):
+    state = cirq.StabilizerStateChForm(0)
+    args = cirq.ActOnStabilizerCHFormArgs(state, [])
+    cirq.act_on(cirq.GlobalPhaseOperation(phase), args, allow_decompose=False)
+    assert state.state_vector() == [[phase]]
+
+
 def test_str():
     assert str(cirq.GlobalPhaseOperation(1j)) == '1j'