The WCF Web API doesn't provide any metadata information you would use to generate a service proxy and thus, be able to add a service reference. It is intended for the easy makingproduction of REST services under the WCF umbrella, just as you do with the ASP.NET MVC 4 Web API framework.
Therefore there is no support for WP7 or Silverlight, but it is almost perfect for the rest of the web.
However, WCF Data Services looks like a right candidate, it allows you to create RESTful services and easily consume 'emthem with Silverlight.