The promising 20-year-old arrived from Everton last summer and, despite not making a single first-team appearance for the Robins last term, has made impressive strides in his development.
Roberts, a Wales Under-21 international, was offered fresh terms in May and boss Mark Yates is delighted to see the stopper has penned a deal for another 12 months.
"We are just glad to have Connor back," he told Town's official website.
"He has developed well working with Steve Book and Browny (Scott Brown) so we didn't want to waste that. The deal had to be right for him but he has made good progress with us, including getting into the Wales Under-21 squad.
"It was touch and go at one stage but we left the door open for him and he's decided to stay."