The left-back, who has started all four of the Robins' matches so far this season, was initially on loan from Macclesfield until January.
"We like what we've seen and it's great to sign Craig permanently," manager Mark Yates told the club's official website.
"It was the right move for ourselves, Macclesfield and Craig himself. He has done well since joining us on loan and there's a lot more to come too. The hard work starts here and Craig is ready for that."
Braham-Barrett made 46 appearances for Macclesfield last season but joined the Robins on loan at the start of the season.