Shuck, a left-handed hitter, batted .167 with two homers and nine RBIs in 22 games this season for Los Angeles. He spent most of the season at Triple-A Salt Lake, where he hit .320 with five homers and 57 RBIs in 102 games. The Angels designated him for assignment Tuesday.
Shuck, 27, batted .293 with 20 doubles, two homers, 39 RBIs and eight stolen bases in 129 games for Los Angeles last season. He's expected to join the Indians during Friday night's game against the Chicago White Sox.
Shuck is from Galion in central Ohio and played at Ohio State. He was drafted in the eighth round by Houston in 2008.