Williams, 24, quit the Iron last summer to join Reading on a Bosman transfer but has failed to establish himself in the first-team picture at the Madejski Stadium.
He started the Royals' first five games of the season - including the 2-1 loss to Scunthorpe on the opening day of the campaign - but has not played since. He made three appearances on loan at the League One side Peterborough in November.
"He's a natural left-sider, who provides good pace, which the team needs. He's been with us as well and is a player we know a lot about," said Tony Daws, the caretaker Iron manager.
"He will bring us a different option as we go forward because he gets up and down that line. He hasn't done as well as he'd have liked at Reading so coming back to familiar territory might get the best out of him."