diff --git a/redis/commands/core.py b/redis/commands/core.py
index 6e1af05635..9793809858 100644
--- a/redis/commands/core.py
+++ b/redis/commands/core.py
@@ -56,7 +56,9 @@
 
 if TYPE_CHECKING:
     import redis.asyncio.client
+    import redis.asyncio.cluster
     import redis.client
+    import redis.cluster
 
 
 class ACLCommands(CommandsProtocol):
@@ -5914,7 +5916,11 @@ class Script:
     An executable Lua script object returned by ``register_script``
     """
 
-    def __init__(self, registered_client: "redis.client.Redis", script: ScriptTextT):
+    def __init__(
+        self,
+        registered_client: Union["redis.client.Redis", "redis.cluster.RedisCluster"],
+        script: ScriptTextT,
+    ):
         self.registered_client = registered_client
         self.script = script
         # Precalculate and store the SHA1 hex digest of the script.
@@ -5930,7 +5936,7 @@ def __call__(
         self,
         keys: Union[Sequence[KeyT], None] = None,
         args: Union[Iterable[EncodableT], None] = None,
-        client: Union["redis.client.Redis", None] = None,
+        client: Union["redis.client.Redis", "redis.cluster.RedisCluster", None] = None,
     ):
         """Execute the script, passing any required ``args``"""
         keys = keys or []
@@ -5979,7 +5985,9 @@ class AsyncScript:
 
     def __init__(
         self,
-        registered_client: "redis.asyncio.client.Redis",
+        registered_client: Union[
+            "redis.asyncio.client.Redis", "redis.asyncio.cluster.RedisCluster"
+        ],
         script: ScriptTextT,
     ):
         self.registered_client = registered_client
@@ -6001,7 +6009,9 @@ async def __call__(
         self,
         keys: Union[Sequence[KeyT], None] = None,
         args: Union[Iterable[EncodableT], None] = None,
-        client: Union["redis.asyncio.client.Redis", None] = None,
+        client: Union[
+            "redis.asyncio.client.Redis", "redis.asyncio.cluster.RedisCluster", None
+        ] = None,
     ):
         """Execute the script, passing any required ``args``"""
         keys = keys or []
@@ -6234,7 +6244,10 @@ def script_load(self, script: ScriptTextT) -> ResponseT:
         """
         return self.execute_command("SCRIPT LOAD", script)
 
-    def register_script(self: "redis.client.Redis", script: ScriptTextT) -> Script:
+    def register_script(
+        self: Union["redis.client.Redis", "redis.cluster.RedisCluster"],
+        script: ScriptTextT,
+    ) -> Script:
         """
         Register a Lua ``script`` specifying the ``keys`` it will touch.
         Returns a Script object that is callable and hides the complexity of
@@ -6249,7 +6262,9 @@ async def script_debug(self, *args) -> None:
         return super().script_debug()
 
     def register_script(
-        self: "redis.asyncio.client.Redis",
+        self: Union[
+            "redis.asyncio.client.Redis", "redis.asyncio.cluster.RedisCluster"
+        ],
         script: ScriptTextT,
     ) -> AsyncScript:
         """
diff --git a/tests/test_asyncio/test_scripting.py b/tests/test_asyncio/test_scripting.py
index b8e100c04a..95e0c80e85 100644
--- a/tests/test_asyncio/test_scripting.py
+++ b/tests/test_asyncio/test_scripting.py
@@ -1,6 +1,8 @@
 import pytest
 import pytest_asyncio
 from redis import exceptions
+from redis.asyncio.cluster import RedisCluster
+from redis.commands.core import AsyncScript
 from tests.conftest import skip_if_server_version_lt
 
 multiply_script = """
@@ -150,3 +152,25 @@ async def test_eval_msgpack_pipeline_error_in_lua(self, r):
         with pytest.raises(exceptions.ResponseError) as excinfo:
             await pipe.execute()
         assert excinfo.type == exceptions.ResponseError
+
+
+class TestAsyncScriptTypeHints:
+    """Tests for AsyncScript type hints with RedisCluster support."""
+
+    @pytest.mark.asyncio()
+    async def test_async_script_with_cluster_client(self):
+        """Test that AsyncScript class accepts RedisCluster as registered_client.
+
+        This verifies the type hints fix for register_script to support RedisCluster.
+        We use a mock-like approach since we don't need actual cluster connection.
+        """
+        from unittest.mock import MagicMock
+
+        # Create a mock RedisCluster instance
+        mock_cluster = MagicMock(spec=RedisCluster)
+        test_script = "return 1"
+
+        # AsyncScript should accept RedisCluster without type errors
+        script = AsyncScript(mock_cluster, test_script)
+        assert script.registered_client is mock_cluster
+        assert script.script == test_script
diff --git a/tests/test_scripting.py b/tests/test_scripting.py
index 899dc69482..ca8eeac5e4 100644
--- a/tests/test_scripting.py
+++ b/tests/test_scripting.py
@@ -1,6 +1,7 @@
 import pytest
 import redis
 from redis import exceptions
+from redis.cluster import RedisCluster
 from redis.commands.core import Script
 from tests.conftest import skip_if_redis_enterprise, skip_if_server_version_lt
 
@@ -53,6 +54,22 @@ def test_encoder(self, r, script_bytes):
         assert encoder is not None
         assert encoder.encode("fake-script") == b"fake-script"
 
+    def test_script_with_cluster_client(self, script_str):
+        """Test that Script class accepts RedisCluster as registered_client.
+
+        This verifies the type hints fix for register_script to support RedisCluster.
+        We use a mock-like approach since we don't need actual cluster connection.
+        """
+        from unittest.mock import MagicMock
+
+        # Create a mock RedisCluster instance
+        mock_cluster = MagicMock(spec=RedisCluster)
+
+        # Script should accept RedisCluster without type errors
+        script = Script(mock_cluster, script_str)
+        assert script.registered_client is mock_cluster
+        assert script.script == script_str
+
 
 class TestScripting:
     @pytest.fixture(autouse=True)