Duffy, 25, who has scored 15 goals in 67 league games for Rovers, will remain at Brunton Park until the final week of the season.
Carlisle manager Greg Abbott said: "We want him to come here and play the way that we know he can.
"He has a good scoring record at this level and he's a quick and alert forward. We think he'll improve what we already have and help us as we go towards a run of very tough games.
"He's another that we are looking forward to working with."