The 25-year-old joined the London Road club in time to appear for their reserves against Northampton Town and he is set for his first team debut against Luton Town on Saturday.
The central defender's move is with a view to a permanent transfer to the Second Division club, should he succeed during his four-week stay with The Posh, after falling out of favour at Millmoor.
Peterborough boss Barry Fry will hope Branston's addition will help the club pull away from the Division Two drop zone, with The Posh currently four points adrift of safety.
