The 29-year-old, who began his career at Leicester City, had been available on a free transfer after leaving Orient at the end of last season.
"We think this is a really good one for us. Leon has played regular football wherever he's been and he's keen to carry that on," Carlisle manager Greg Abbott told the club's official website.
"He joined us for training today and you could see he's fit and raring to go. He has good knowledge of this level and he wants to be playing football. He's a player who can do a number of jobs and he's one we are really looking forward to working with."
McSweeney will now remain with the club until at least January.