A listing for a multi-platform Pacific Rim video game has shown up on the Austrailian Classification website. It is being developed by Yukes and is currently sporting an M rating for Fantasy violence. From the screenshots that have been leaked it looks like it will be a multiplayer brawler. Yukes also created the video game for Real Steel so if you have played that game this looks like it could be running the same engine.
The movie is launching on July 12th so the best bet for the game would be slightly before or slightly after. You can check out some of the screenshots that have leaked online here.