Fix call async routes decorated with class based decorator

fastapi/routing.py

@@ -208,7 +208,12 @@ def get_request_handler(
     dependency_overrides_provider: Optional[Any] = None,
 ) -> Callable[[Request], Coroutine[Any, Any, Response]]:
     assert dependant.call is not None, "dependant.call must be a function"
-    is_coroutine = asyncio.iscoroutinefunction(dependant.call)
+    if inspect.isfunction(dependant.call):
+        is_coroutine = asyncio.iscoroutinefunction(dependant.call)
+    else:
+        is_coroutine = asyncio.iscoroutinefunction(
+            getattr(dependant.call, "__call__", dependant.call)  # noqa: B004
+        )
     is_body_form = body_field and isinstance(body_field.field_info, params.Form)
     if isinstance(response_class, DefaultPlaceholder):
         actual_response_class: Type[Response] = response_class.value

tests/test_endpoint_with_async_class_decorator.py

@@ -0,0 +1,32 @@
+from functools import update_wrapper
+
+from fastapi import FastAPI
+from fastapi.testclient import TestClient
+
+
+class SomeDecorator:
+    def __init__(self, original_route):
+        update_wrapper(wrapper=self, wrapped=original_route)
+        self.route = original_route
+
+    async def __call__(self, *args, **kwargs):
+        return await self.route(*args, **kwargs)
+
+
+data = {"working": True}
+
+
+@SomeDecorator
+async def route():
+    return data
+
+
+app = FastAPI()
+app.get("/")(route)
+
+client = TestClient(app)
+
+
+def test_endpoint_with_async_class_decorator():
+    response = client.get("/")
+    assert data == response.json()