The 26-year-old joined the Robins from Tamworth last summer and has made one start and seven substitute appearances for the club.
His only full game was against Oxford United in the 2-0 Johnstone's Paint Trophy first round win, when he operated at right wing-back.
"I'd like to wish Andy all the best at Barrow," Cheltenham Town boss Paul Buckle said. "He hasn't played enough football for the last few years and he needs to go somewhere and play regularly now."
Barrow currently lie second in their division, five points behind leaders AFC Fylde. They play Oxford City away on Saturday,