The Minnesota Twins drafted him with the 1,273rd pick in the 2001 Major League Baseball draft. He declined to sign with Minnesota, and instead enrolled at Louisiana State University (LSU) to play college baseball for the LSU Tigers. As a freshman at LSU, Vargas had a 1–1 win-loss record with a 3.43 earned run average in 13 games. He also saw occasional playing time as a first baseman and designated hitter. In his first college at bat, he launched a pinch hit grand slam to lift the Tigers to a victory over Mercer.