He returned to the Blues at the end of the initial loan to be assessed by their staff, but will now see out United's Championship campaign.
He is expected to be available for selection in Saturday's FA Cup third round clash against Preston North End at Deepdale.
Since joining United, Cork is featured in 17 games and scored one goal.
The Iron have relied heavily on loan signings this season, with manager Nigel Adkins currently trying to re-sign full-back Kelly Youga from Charlton and striker Tomi Ameobi from Leeds.
Charlton have recalled Youga following his loan at Glanford Park and expect to play him in the FA Cup this weekend, though Adkins is hopeful of securing his return before the end of the January transfer window.