The 20-year-old, who played for the League One side in a friendly against Rangers in October, has initially joined the Cumbrians until January 1.
"I'm very happy. Craig is a player I have watched a lot and he has a huge amount of potential," Carlisle boss Graham Kavanagh told the club's official website.
"Hopefully he'll get up to speed as quickly. He played really well in the game we won against Rangers last month."
Roddan is yet to make a first-team appearance for Liverpool.