The 21-year-old's Hillsborough contract was terminated by mutual consent.
Warnock told the club's website (www.sufc.co.uk): "His career has taken a backward step, both on and off the field. But we feel he is worth an opportunity to resurrect himself until the end of the season."
Morrison came through the Owls YTS scheme three seasons ago and was said to be the next thing since bread but like the team his talents turned stale.
This season he has failed to create a impression in front of both Terry Yorath nor Chris Turner and was forced to move to Carlisle United on loan in order to re-start his football career but he failed to make a impact.