Thome, a member of the 600-homer club, had been sidelined with a lower back strain since April 29. He's just 2 for 18 in limited appearances, mainly as a pinch hitter. Thome could get plenty of at-bats as a designated hitter in nine interleague games upcoming.
Orr hit .286 (12 for 42) with four extra-base hits and five RBIs.
The move was made before Wednesday night's game against the Los Angeles Dodgers and Thome was available to play.