You already have it. It's called the Operating System. The cat is more interested in pushing the mouse around (as they do!) than playing a computer game. Especially if it's an Apple Mac because the operating systems are called things like Tiger, Snow Leopard, etc.
If you feel confident that the cat can use the Internet without doing something like accessing Kitty Porn or downloading movies like "The Truth About Cats and Dogs", "Cat On A Hot Tin Roof" and "Crouching Tiger Hidden Dragon" or the complete soundtrack of the musical "Cats" and blowing your download limit then consider the more popular web browsers:
Internet Explorer: cats are curious, they like to explore, your cat will love it!
Mozilla Firefox: cats don't like fire or foxes, it'll probably not use it!
Safari: all cats think they are just miniature lions, it'll be rapt!
Google Chrome: cats are engrossed with shiny glittery thngs, it'll spend hours using it (and probably use your download limit too!)