Williams, 24, trained with Posh on Friday and is in line to make his debut against Charlton Athletic on Saturday.
He has made just five appearances for the Royals, including his debut against the Iron on the opening day of the season.
"Marcus has played a number of games and there's always a transition when you come to a new club. He's out of our team at the moment but it's important he's up to speed and ready," said nick Hammond, director of football at Reading.
"A month playing at the top end of League One is important for him in terms of games, and it's a good move."
The move has reunited Williams with the midfielder Grant McCann, who he played alongside at Scunthorpe but also left after he rejected a contract extension.