The 17-year-old, who stands at 6ft 4in, is tough and uncompromising and has featured regularly at reserve team level.
Shires, who has played for Worksop Town and Hallam in previous years, joined Evo-Stik Division One (South) side Carlton Town on a one-month loan in February 2015.
He scored on his second appearance for the Millers in a victory over Kidsgrove Athletic.
