The 32-year-old has been without a club since leaving Newcastle in the summer and had retired from the game, but had been on trial with Blues for the past couple of weeks.
Manager Alex McLeish has now agreed a deal to sign the right-back and he will be able to face Crystal Palace subject to receiving confirmation from the Football League.
McLeish said: "We've been looking to strengthen the full-back position and are pleased to bring in Stephen as he brings with him great experience.
"He has not played for a while but there's no doubt he is a quality player who can definitely bring something to the side once he is fully match fit."
Carr later received clearance from the Football League and is therefore eligible to play against Palace, if selected.