The 26 year old defender has been allowed to leave Ibrox in search of first-team football after suffering a series of injuries since his arrival on loan from Wigan in January 2007.
Gers boss Walter Smith told the club's official website: "We have allowed Andy to go on loan to Bristol City until the January transfer window.
"We feel it will be beneficial for him to get first-team football there and we hope he can return to the level we all know he is capable of.
"Andy has had a torrid time since he arrived at Rangers and it will be good for him to get games every week in another environment."