Microsoft has released its Xbox app with name My Xbox LIVE for iOS Devices. Application which is already available at App Store has been designed mainly for two different types of iOS devices. One will run on iPhone and iPod Touch whereas other one is specially designed for iPad with larger screen support.
From App Store:
Take your Xbox LIVE experience wherever you go with the My Xbox LIVE app. Track and compare your achievements, connect with your Xbox LIVE friends, and change up your 3D Avatar. Review all your recent great games you and your friends love to play and compare achievements with them. Jump into our games hub to learn about the latest LIVE games and apps. Access Xbox Spotlight feeds, get breaking news from Xbox LIVE, game tips and tricks, gamer spotlight and much more.
You can download the application from App store at free of cost and it is compatible with iPhone, iPad and iPod Touch devices running iOS 4.3 or later