Rothery, 19, made his Carlisle debut in the Easter Bank Holiday Monday defeat at Huddersfield Town, having joined the club on a trial basis during the January transfer window.
The Cumbrians have offered new two-year deals to Danny Graham, David Raven, Tony Kane and Ian Harte along with Workington goalkeeper Adam Collin while former York midfielder Gavin Rothery has been handed a one-year deal.