The Carcassonne game on Aso Brain is called Toulouse. You need to register on the site with a user name and password. You can then choose the ranked, tournament, or unranked game lobbies. If you have not played Carcassonne previously you will want to choose unranked and then start a game with just bots (computer opponents) until you get the hang of the game.
When you start playing human opponents it gets to be a very fun and addicting time waster. I play the actual "real world" Carcassonne tile game almost every day over lunch with friends. The online version will give me a chance to hone my skills.