Rovers hope to have the player available for the League One clash with Colchester United at the Keepmoat Stadium on Saturday afternoon.
The 29-year-old started his career at Nottingham Forest before joining Macclesfield.
Sinclair has just completed a short-term loan at Barnsley. He will wear the number 18 shirt for Rovers.
"Doncaster Rovers are pleased to announce the signing of Peterborough United striker Emile Sinclair," a statement from Rovers read.
"Sinclair, who will be available for this afternoon's game subject to paperwork clearance by the Football League, has signed a loan deal with the club until the end of the season.
"This season, Sinclair has a hat-trick to his name after scoring all three goals in Peterborough's first league victory which came against high-flying Hull City."