The Broncos also waived tackle Matt Murphy, whom they had signed on Monday.
Cutler's original backup, Patrick Ramsey, was lost for the season Oct. 20 with an elbow injury.
Hackney is a second-year pro out of Alabama-Birmingham who also was promoted off Denver's practice squad last season. Although he was active for the final eight games, he has yet to appear in an NFL regular-season game.
Hackney completed 24 of 38 passes for 285 yards and a touchdown in the preseason.