Rogers graduated from Plant City High School in Florida in 1982, where he played baseball only during his senior season, hitting .375 as a right fielder (he played shortstop in his senior league). He was selected by the Texas Rangers in the 39th round of the 1982 Major League Baseball draft, and signed for $1,000. He was converted into a pitcher on the strength of his throwing arm and left-handedness. Rogers spent 7 years in the minor leagues before making it to the Rangers in 1989 as a reliever. He became a starting pitcher for the club in 1993.