Swift was in uniform Wednesday night when the Suns visited the Miami Heat, but did not play.
Swift was waived earlier this week by the New Jersey Nets. The nine-year veteran averaged only 3.8 points in six games with the Nets this season, but the former LSU standout could be vital to Phoenix, which may be without Stoudemire (eye surgery) for the remainder of the season.
"We are very pleased to be able to add a player of Stromile's caliber at this late date," Suns president and general manager Steve Kerr said. "We believe that his athleticism, length and experience will be valuable to us as we head down the stretch run."