Service Broker is a queuing system so won't be calling out as you might be thinking of it. You can attach to the queue an "activation stored procedure" that the system can invoke for you but that procedure is obviously running on the database server.

At the end of the day if you want a C# app outside the database to run when something is added to the queue you C poll the queue yourself looking for messages or you can do an internet search for"service broker external activation" which tried to handle the polling piece for you.