Barría signed with the Los Angeles Angels for $60,000 as an international free agent in 2013. He made his debut that same year with the Dominican Summer Angels of the Rookie-levelDominican Summer League, pitching in five innings and giving up six earned runs. He returned there in 2014 where he improved, going 4–4 with a 3.03 earned run average (ERA) in 16 games (eight starts). In 2015 he played for both the Arizona Angels of the Rookie-level Arizona League and the Orem Owlz of the Advanced Rookie-level Pioneer League, pitching to a combined 5–4 record and 4.02 ERA in 15 games (14 starts). He pitched in 2016 for the Burlington Bees of the Single–AMidwest League and was named the Angels' Pitching Prospect of the Year by MLBPipeline.com after he compiled an 8–6 record and 3.85 ERA with a 1.32 WHIP in 25 starts.[1]
After he made one start for the Bees in 2018, the Angels promoted Barría to the major leagues on April 11, 2018, to make his debut against the Texas Rangers.[4]
On April 22, 2018, Barria faced Brandon Belt of the San Francisco Giants who had an at bat that lasted 21 pitches before ending with a fly out to right field, breaking the MLB record for most pitches to a single batter in a single at bat.[9] On the season, Barría started 26 games for the Angels, going 10–9 with a 3.53 ERA with 98 strikeouts in 129+1⁄3 innings.[10] He was the fifth-youngest player in the AL.[10] In 2020, he went 1–0 in 7 games (5 starts).
On January 13, 2023, Barría signed a one-year, $1.05 million contract with the Angels, avoiding salary arbitration.[11] In 34 appearances for the Angels, he struggled to a 2–6 record and 5.68 ERA with 62 strikeouts in 82+1⁄3 innings of work. Following the season on October 16, Barría was removed from the 40–man roster and sent outright to Triple–A Salt Lake. He subsequently rejected the assignment and elected free agency.[12]
Cleveland Guardians
On December 1, 2023, Barría signed a minor league contract with the Cleveland Guardians.[13] In 13 games for the Triple–A Columbus Clippers, Barría compiled a 4.81 ERA with 27 strikeouts across 24+1⁄3 innings pitched.[14]