The code is available on Github here.
The project has two controllers: HomeController and RecordController. HomeController is the ASP.Net MVC controller while RecordController deals with Web API. The Web API data infrastructure is in /Models folder. The script file is in /Scripts/Home/record.js. One last thing I need is a view, so there is a view RecordsApi.cshtml under /Views/Home
The view has all the regular angular directives. It uses /Scripts/Home/records.js file which has all the Angular.js stuff. I use $http service to communicate with the server.
In short, ajax calls are replaced with calls to the corresponding methods of Angular's $http service. The view is created as usual, API controller is the same as it would be for a regular Web API service, and models are done in the same way. The only difference you need to make if you want Angular.js front-end is to introduce angular script in the view and put all the directives in place.
Comments/questions are welcome.