As already mentioned, F#'s MailboxProcessor class offers a simple, straightforward implementation of the actor model. A fantastic introduction on how to use it is available here. F# interoperates with C# very well and you can wrap up the agent in a class with methods which post different messages. For the cases where the agent will reply with an asynchronous response, see the PostAndAsyncReply method. This returns an Async workflow which you can turn into a task that can be awaited in C# using the Async.StartAsTask method.
Finally, if you need to distribute your actors remotely, I recommend you check out Akka.NET which offers both C# and F# APIs.