The 28-year-old goes straight into the Robins squad for this weekend's League Two match at Aldershot.
Carter agreed terms at the club's training ground on Thursday morning.
"We're delighted. He has experience and a lot of quality," manager Mark Yates told the club's official website.
"It's known that I've been after a midfield player and patience has paid off.
"We're looking forward to getting him up to speed and getting him involved."