Tournaments are not available yet on iOS but they are working on it. You could play through the browser and I've heard you can sign up for a tourney in the browser, then get into live on the app and your games can be played there.
I don't know how well it works in practice and I don't know if that is officially supported or might stop working at some point.
Hi, does anyone know if it is possible to join and play in tourmanents with the chess.com IPhone App?
It is difficult for me to play 1-min bullet chess using the mouse on PC. I can play faster/better with the IPhone chess.com App.