ASP.NET Identity in a Web API

It depends on what authentication method you are using. Most of the web applications use Form (Cookie) authentication module as primary authentication method. It should work fine with your web pages, but it isn't the best choice if you want to work with your API on the native client like a mobile app. You should be careful with CSRF attack when enabling cookie authentication with web api.

Supposing that you are using cookie authentication, you still have two choices. One is FormsAuthentication IIS module, which is quite old, you should use FormsAuthentication.SetAuthCookie to sign in the user.

The other way is OWIN cookie middleware, which is used in default MVC 5 template to support authentication. Please check my answer on how to sign in user by OWIN API

If you want to have a better authentication story for web API with mobile app, I will suggest you to use the OWIN OAuth middleware to enable bearer token as primary authentication method for web api. In MVC 5 SPA template, it demonstrates a good pattern to use them together along with MVC and cookie auth. My blog Understanding Security Features in the SPA Template for VS2013 RC should give a general idea on how they are working together.

The identity framework has an OWIN package which implements most of the OWIN authentication code. So you don't need to implement your own. Why not use it?