Wagner was selected in the first round of the Major League Baseball draft in June 1993 by the Houston Astros. He pitched exclusively as a starting pitcher in Minor League Baseball for the Quad Cities River Bandits, until his major league debut. In 1994, Wagner led all North American minor league pitchers in strikeouts, with 204. Wagner made his first Major League appearance with the Astros, as a late-season promotion from AAA baseball, on September 12, 1995, pitching against one batter late in a 10–5 defeat by the New York Mets. This was his only opportunity to pitch for the Astros that season.