The 20-year-old has enjoyed previous loan spells with Hereford, Notts County, Swindon, where he scored five goals in 14 appearances, and Preston.
Jervis will not be eligible to play in any Capital One Cup fixtures for the Cumbrians, but will be available for the Johnstone's Paint Trophy first-round match against Preston.
Manager Greg Abbott told the club's official website: "Jake is one we've know about for a while.
"He's got some good loan spells under his belt already and he is hungry for some first team action.
"We think he'll add something a little bit different and we're looking forward to working with him."