On July 27, 2018, Alcalá and Gilberto Celestino were traded to the Minnesota Twins in exchange for Ryan Pressly. He was assigned to the Chattanooga Lookouts. In 24 games (16 starts) between Buies Creek, Corpus Christi, and Chattanooga, he pitched to a 3–11 record with a 3.81 ERA and a 1.34 WHIP. He split the 2019 minor league season between the Pensacola Blue Wahoos and the Rochester Red Wings, combining to go 6–7 with a 5.47 ERA over 109 innings.
