Putnam was selected by the Texas Rangers in the first round of the 1975 Major League Baseball draft. He had been drafted a year earlier by the New York Mets, but did not sign. Putnam batted only .242 his first professional season in the Rangers' farm system; however, his batting average jumped to .361 with 24 home runs in . After batting .301 with 15 home runs and 102 runs batted in for the Triple A Tucson Toros in , Putnam made his Major League debut as the designated hitter batting fourth against the Boston Red Sox on September 2.