Can a bad gas cap cause a engine misfire?

A gas cap should not make the car misfire, i would get a free diagnostic from autozone to see what the problem is.

This vehicle may still have an emissions warranty, so if the check engine light is on I would take it to the dealer and get it addressed. You can take it to Autozone and let them read the codes in the engine control module, but these are merely clues as to what diagnostic tests need to be performed and is in no way a "diagnosis". Have a professional perform the diagnosis if you wish to get your vehicle repaired properly.