As of April 2015, the game SPINTIRES is not available for the Xbox 360. The developers most likely won't make a version as the system is outdated and no longer officially supported.
SPINTIRES is available for PCs running Windows 7 or newer. It is possible to connect an Xbox 360 controller to a PC to play the game using the USB adapter normally included with new controllers. The game is a digital download title and available through gaming services, such as Steam and Amazon Digital Downloads. Oovee has not announced any plans to port the game to any console systems.