The 29-year-old, who can also play right-back, scored one goal in 23 appearances after joining the Devon club from Kidderminster in November.
"He's an athlete that can play anywhere and I'm delighted to have him back on board," said manager Kevin Nicholson.
"Aman was a valuable asset for us last season and is a fantastic guy to have on and off the pitch."
Verma will remain at Plainmoor alongside striker Nathan Blissett, who signed a deal on Wednesday.
Torquay United midfielder Aman Verma has agreed terms on a new contract with the National League side.