I have a little bit of a \"strange practise\" question. The requirement on an architecture of our project is to setup Web API with (if possible) all MVC goodness within WCF
It is possible but with losing the MVC goodness (that means that you will not be able to use for example the built in automatic online documentation for your web services).
Just install Web API through NuGet and then register your route in global.asax. Create your api controller and it should be all good.
EDIT 01.02.2017:
This is no longer true. Since Microsoft approach was to merge MVC and Web API controller. Now anything is possible.