Hunter, a right winger, has put pen to paper on a two-year deal which will take effect from his 17th birthday.
Hunter has been involved with the Rovers first-team squad on several occasions but has yet to make a senior appearance for the club.
"Shaquille is a gifted player with great one-on-one ability and he is definitely a player who will excite," head of youth Ken Oram told Rovers' official website.
"It is great to see a Bristol boy do well and it is fantastic recognition for the work that goes into our youth programme. It is fantastic that Shaquille has worked hard and been rewarded with this contract."
Chairman Nick Higgs added: "We are delighted that Shaquille has signed his first professional contract with us. He is a really exciting prospect and we are pleased that he has committed his future to us."