There's nothing built-in in the CF that provides web server capability. Windows CE has always shipped with an HTTPD server, but, honestly, it sucks and can't be integrated with managed code anyway.
We solved this problem long ago by creating our own IIS-like web server implementation (available commercially). You could do something similar as well - it's just a lot of Socket work. That trivializes the complexity of concurrent request handling and providing an IIS-like object model, but you get the idea. Basically you have to write the whole thing.