Shaw signed a minor-league contract with the Angels on Wednesday, Jeff Fletcher of The Orange County Register reports.
He can earn a prorated $1.1 million if he's in the majors, per Fletcher. Shaw allowed five runs (four earned) over four innings for the White Sox this season before getting removed from their 40-man roster and later electing free agency. The 36-year-old reliever will presumably head to Triple-A Salt Lake for now but could get a look when the Angels need a fresh bullpen arm.