From what I've learned, Microsoft did a little bit of naming confusion here.
I'm assuming you know what WCF is all about, this big framework built on top of XML to allow user to build distributed services with a wide variety of technologies (from SOAP to REST to MSMQ etc.).
It's hard as hell to use (for me at least) and requires a lot of bootstrap to have it working, and eventually they realized this and started providing some default configuration for simple http services (WCF REST starter kit anyone?). ASP.NET MVC was gaining momentum and some of the features it provided (automatic arguments matching for example) started to show up in WCF.
Now that's the situation:
Announcement: WCF Web API is now ASP.NET Web API! ASP.NET Web API
released with ASP.NET MVC 4 Beta. The WCF Web API and WCF support for
jQuery content on this site wll removed by the end of 2012.
http://wcf.codeplex.com/wikipage?title=Getting%20started:%20Building%20a%20simple%20web%20api
And that's better imho.
I'm quite sure it should be possible to host asp.net mvc4 webapi on top of WCF (if you ever need that), but i can't find documentation that can prove me right (or wrong).
UPDATE (can't fit as comment):
Wait, there is a huge different between "moving a subset of communication technology from a library/framework to another" and "replace WCF". I personally think that WCF was designed for some kind of communication concept and it has a rather cool design, but the distributed computing is somewhat moving on to new (and simpler) solutions (look the feature-rich SOAP vs the lean e flexible REST, although many people still use REST in a RPC manner), and i think that this kind of programming patterns better fit into the MVC architecture than the WCF one. Effort was put on designing some simple way of building/consuming web services on top of WCF, but they eventually found out that it was not the right solution.
Not to mention that many developers now use ASP.NET MVC and want to do rest web services for their web app, messing with WCF is often overkill for these kind of things, and I've experienced that on my own skin.
I think that the routing mechanism is awesome and the right way to go, and if you look closely, they included part of it (with different names and types, but the pattern was there) in WCF. So yeah, i think that if MS don't dismiss that part of WCF WE should do it. To strictly answer, no, i don't think you'll ever find WebGet/WebInvoke in asp.net mvc*, it just don't fit in.
Yeah self-host is probably the only bit of WCF contained in ASP.NET MVC4 right now.