Guthrie will be assigned to Triple-A El Paso.
He was granted his release by the Texas Rangers on Monday.
The 36-year-old Guthrie signed a minor league deal with Texas right before spring training. He had a 5.14 ERA in three Cactus League appearances, allowing three home runs with five strikeouts over seven innings. In a Triple-A game last week, he gave up three solo homers over five innings.
Guthrie started Game 7 of the 2014 World Series for Kansas City but was left off the Royals' postseason roster last season.
He is 91-108 with a 4.37 ERA in 305 career games for Cleveland, Baltimore, Colorado and Kansas City.