The Giants claimed Jackson from waivers Tuesday, Dan Salomone of the Giants' official site reports.
Jackson was signed to the Browns' active roster Saturday, played seven snaps on special teams Sunday against the Colts and was cut by the team Monday. Rather than going unclaimed, Jackson was picked up by the Giants, who are in need of backfield depth with Eric Gray (calf) placed on injured reserve, while Saquon Barkley (elbow) and Gary Brightwell (hamstring) are both questionable for the Week 8 game against the Jets.