There's a listing for Theatrhythm: Final Fantasy up on the New Zealand iTunes Store, which almost certainly means that the rhythm game will be out in North America later today.
Theatrhythm is a tap-tap-tap game in the style of Elite Beat Agents or Guitar Hero in which you strum your fingers across the screen to the beat of Final Fantasy music. It's quite fun.
Square has yet to make an official announcement about the iOS port of Theatrhythm, but this version is a free app that comes with a couple of songs and asks you to pay for the rest. And of course it has Twitter integration, because why even play games these days if they don't have Twitter integration?