The 26-year-old midfield man has only made 18 appearances in his entire career, including three during a loan spell at Motherwell.
He has signed a six-month contract with the Cumbrian outfit.
United boss Paul Simpson said: "It is a significant coup for the club as we look to establish ourselves back in the Football League.
"It's now up to Jamie to show us what he can do, and deal with the competition within the squad."