On July 29, 2021, the Yankees traded Alcántara and Alexander Vizcaíno to the Chicago Cubs in exchange for Anthony Rizzo.[3][4] He was subsequently assigned to the rookie–level Arizona Complex League Cubs. Alcántara spent the 2022 campaign with the Single–A Myrtle Beach Pelicans, slashing .273/.360/.451 with 15 home runs, 85 RBI, and 14 stolen bases.[5][6] On November 15, 2022, the Cubs added Alcántara to their 40-man roster to protect him from the Rule 5 draft.[7]
Alcántara was optioned to the High–A South Bend Cubs to begin the 2023 season.[8] In 95 games for South Bend, he batted .286/.341/.466 with 12 home runs, 66 RBI, and 15 stolen bases. Alcántara was optioned to the Double–A Tennessee Smokies to begin the 2024 season.[9] During the season, the Cubs promoted him to the Triple–A Iowa Cubs.
On September 25, 2024, the Cubs promoted Alcántara to the major leagues and he made his major league debut that night.[10]