The 28-year-old left-back had made just five League One appearances so far this season since signing on the transfer deadline day in August.
The Argentinian defender has been playing in English football since June 2008 with spells at Swansea, Leeds, Charlton and the Robins.
"Bessone has already travelled back," manager Paolo Di Canio told the club's official website. "He already asked me to go back because he knows that the contract has finished. Jay (McEveley) is back and we don't need to keep him."