The 18-year-old had been unable to head to Glanford Park before the season got underway as he was in Malaysia for the World Youth Club Championships, and was part of the Blues squad which travelled to America in pre-season.
He played seven games on loan at League One side Bournemouth last term.
"I talked to a number of different clubs, but decided Scunthorpe was the best option for me," he said.
"It is a good young team and I think we will do really well, I'm looking forward to the challenge."
Cork will wear shirt No.16, although United will assess his fitness following two lengthy trips away before considering naming him in the squad to face Burnley on Saturday.