I had the same question three months ago. I spent many hours researching the best PHP frameworks to use. In the end I settled on Laravel.
Right out of the box it comes with RESTful routes and controllers, and easy to use authentication. I had a simple REST API up and running in about a day
http://laravel.com/docs/routing#the-basics
http://laravel.com/docs/controllers#restful-controllers
It also comes with a great ORM which makes setting up resources super easy
http://laravel.com/docs/database/eloquent
I am using version 3.2 and it works like a charm and is stable. Version 4 is still in beta, but does have a lot more REST orientated features (i think one is that it makes it easier to create resources from within your controllers)
Great tutorial here http://net.tutsplus.com/tutorials/php/laravel-4-a-start-at-a-restful-api/