After the 2011 season, he played collegiate summer baseball with the Yarmouth–Dennis Red Sox of the Cape Cod Baseball League. Appel was named a First Team All-American before the 2012 season. As a junior, he pitched to a 10–2 record and 2.56 ERA, and won the National Pitcher of the Year Award. Appel was projected as a potential first overall pick in the 2012 Major League Baseball Draft, but reportedly rejected an offer from the Astros for a $6 million signing bonus. Due to the high perceived bonus demands, Appel fell in the draft to the 8th overall selection, where he was chosen by the Pittsburgh Pirates. However, Appel did not sign with the Pirates before the July 13, 2012, deadline and instead played his senior year at Stanford. He turned down an offer of a $3.8 million signing bonus. Appel graduated from Stanford after the fall semester, receiving a degree in Management Science and Engineering. For the Cardinal baseball team, Appel pitched to a 10–4 record with a 2.12 ERA and struck out 130 batters in innings. The Pac-12 Conference honored him as their Scholar-Athlete of the Year. Appel was selected by the Houston Astros with the first pick in the 2013 Major League Baseball Draft. On June 19, he signed with the Astros for a signing bonus worth $6.35 million. Appel made his professional debut in July with the Tri-City ValleyCats of the Class A-Short Season New York–Penn League. After making two starts for Tri-City, the Astros promoted Appel to the Quad Cities River Bandits of the Class A Midwest League. When Appel joined Quad Cities, teaming with Carlos Correa, this marked the first time that two consecutive first overall draft picks played for the same minor league team. The Astros ended Appel's season in August, with approximately 140 innings pitched on the season, between college and minor league baseball. For Tri-City and Quad Cities, Appel pitched to a 3–1 record in 10 games started, with a 3.79 ERA and 33 strikeouts with nine walks in 38 innings. The Astros invited Appel to spring training in 2014 as a non-roster player. Appel underwent an appendectomy in January, which delayed his preparations for the 2014 season. He was reassigned to minor league camp, where he made his spring debut. He started for the Astros in their final spring training game, throwing three scoreless innings against the Rojos del Águila de Veracruz of the Mexican League.