On December 28, 2011, Alcántara was traded with Josh Reddick and Miles Head to the Oakland Athletics in exchange for Andrew Bailey and Ryan Sweeney.[2] He played the entirety of the 2012 season with the Class A Burlington Bees. He returned to Class A in 2013 with the Beloit Snappers, but was promoted to the Class A-Advanced Stockton Ports at mid-season. He was added to the Athletics' 40-man roster on November 20, 2013.[3]
Alcántara began the 2014 season with the Double-A Midland RockHounds, but made only three starts before requiring season-ending Tommy John surgery.[4] He returned to play in 2015, making 15 starts at Class A-Advanced Stockton. He played that off season with the Estrellas Orientales of the Dominican Winter League. He began the 2016 season at Double-A, but was promoted to the Triple-A Nashville Sounds on July 20.[5]
Alcántara was called up to the Athletics to make his major league debut on September 5 against the Los Angeles Angels of Anaheim.[6]
Alcántara started the 2017 season in Oakland, but was designated for assignment on April 25 after accumulating a 16.71 ERA in three appearances.[7] His contract was selected from Nashville, and he was added to Oakland's active roster on September 5.[8] He was cleared waivers and was sent outright to Nashville before the 2018 season. Alcantara elected free agency on October 5, 2018.
KT Wiz
On November 18, 2018, Alcántara signed with the KT Wiz of the KBO League. He became a free agent following the season.
Doosan Bears
On December 23, 2019, Alcántara signed a one-year, $700,000 deal with the Doosan Bears of the KBO League.[9] After the season, Alcántara was named the Choi Dong-won Award Winner, the equivalent to the Cy Young award in the KBO, after pitching to a 2.54 ERA with 8.2 K/9 and 1.4 BB/9 over 198.2 innings pitched.[10] He became a free agent following the season.
On December 11, 2022, Alcantara signed with the Doosan Bears.[12] In 2023, he made 31 starts for Doosan, logging a 13–9 record and 2.67 ERA with 162 strikeouts across 192 innings of work.
On December 21, 2023, Alcántara re–signed with the Bears on a one–year, $1.3 million contract.[13] In 12 starts, he compiled a 2–2 record and 4.76 ERA with 34 strikeouts across 64+1⁄3 innings pitched. Alcántara was released by Doosan on July 4, 2024.[14]