Quiroz made his professional debut for the Tigres de Quintana Roo of the Mexican Baseball League in 2011.

[5] He started the 2018 season with the Double-A Portland Sea Dogs, his first time playing professional baseball outside of Mexico.

[2] The Red Sox traded Quiroz to the San Diego Padres in exchange for pitcher Colten Brewer on November 20, 2018.

[8] Quiroz spent the 2019 season with the Triple-A El Paso Chihuahuas, playing primarily second base, hitting .271/.384/.539/.923 with 19 home runs and 66 RBI.

[10] The 2020 minor league season was cancelled due to the COVID-19 pandemic, but the Rays invited Quiroz to be one of the 60 players in their training pool.

[13] On September 20, Quiroz collected his first MLB hit, a single off of Miami Marlins starter Pablo López.