Firth, 23, has been with the Light Blues since last January after signing an 18-month upon arriving from English National League side Barrow, but he has featured in just one game so far.
The Rangers man came on as a substitute for Wes Foderingham on the final day of last season away to Kilmarnock in May, and has mainly being a training ground goalkeeper.
Nevertheless, the Ibrox outfit deemed it fit to hand him a new deal and he will continue to provide back up for the wantaway Foderingham and Allan McGregor.