Dorsey had to step in after the Browns backup quarterback, Derek Anderson, separated his shoulder during Sunday's game against to Tampa Bay, which the Browns lost to fall to 4-11.
Browns' starting quarterback Charlie Frye hasn't been able to play since he bruised a bone in his right wrist in early December.
"Dorsey's been here all year," said Cleveland Coach Romeo Crennel. "He has a pretty good knowledge of the system. At times he's looked pretty good at practice and I think it's the best alternative under the circumstances."
Dorsey was obtained by the Browns last May in a trade with San Francisco. For his career he has completed 171 of 316 passes for 1,712 yards and has thrown eight touchdowns and 11 interceptions.
The Browns are also likely to sign quarterback Lang Campbell, who has trained with them for the last two seasons.
Notable deaths of 2014 [PHOTOS]