He has represented Mexico in international baseball competitions after previously playing for Cuban youth teams.

[3] During the 2013–14 and 2014–15 seasons, Arozarena played for Vegueros de Pinar del Río of the Cuban National Series.

[9] Following the season, he returned to the Mayos de Navojoa, where he slashed .292/.366/.558 and led the Mexican Pacific League with 14 home runs in 65 games.

[23][24] On January 9, 2020, Arozarena was traded to the Tampa Bay Rays, along with José Martínez and the Cardinals’ competitive balance round A draft pick, for Matthew Liberatore, Edgardo Rodriguez, and the Rays’ competitive balance round B draft pick.

[25] Arozarena started the shortened 2020 season on the COVID-19 minor league injured list,[26] joining the Rays on August 30.

[37] The Rays created a "Randy Land" fan seating section behind Arozarena in left field early in the 2023 season.

[41] On August 31, Arozarena stole third base against the Miami Marlins and became the first MLB player to record three straight 20–20 seasons to begin his career.

[43] Arozarena is the Rays' franchise leader with 59 hit by pitches, one ahead of Brandon Guyer, and ranks in the top 10 in many offensive categories, including home runs, stolen bases, and OPS.

[46] He also holds many Rays postseason records, including most hits, home runs, and total bases,[47] batting .349 in 28 games.

[23] On July 25, 2024, Arozarena was traded to the Seattle Mariners for Brody Hopkins, Aidan Smith and Ty Cummings.

[51] Combined with the Rays and Mariners in 2024, Arozarena slashed .254/.346/.436 with the 20 home runs and 20 stolen bases as well as 60 RBI in 648 plate appearances.

[55] In the semifinal game against Japan, Arozarena hit a double to score the go-ahead run and made several timely catches, including a "home-run robbery" from Kazuma Okamoto.

[56] Arozarena led Mexico in many offensive categories, batting .450/.607/.900 with six doubles, one home run, and nine RBIs in the tournament.

[57] Mexican President Andrés Manuel López Obrador called Arozarena a "phenomenon" for his tournament performance.

[59] Arozarena received his all-tournament award from Mexican Foreign Secretary Marcelo Ebrard at a Rays game on May 21, 2023.

[61][6] Shortly after his father Jesús died, he fled Cuba in June 2015 on a small, broken boat, traveling eight or nine hours to Isla Mujeres, Mexico, where he established residency before signing his first MLB contract.

[63] On November 23, 2020, Arozarena was arrested in Mexico's Yucatán state after allegedly trying to kidnap his daughter from her mother and assaulting the woman's father.

The two outfielders were teammates and roommates in the Cardinals minor league system, and Arozarena described Garcia as "kind of like my brother" in 2023.

[68][69] The two friends both started in the outfield in the 2023 All-Star Game, after Arozarena bested Garcia in the Home Run Derby.