Rodríguez began his professional career in the Mexican League with the Leones de Yucatán, playing for them from 2014 through 2016.

[6] He spent the 2019 season with the Myrtle Beach Pelicans, going 1–3 with a 3.45 ERA and 52 hits, 36 walks, and 65 strikeouts over 45 innings.

[8] Rodríguez opened the 2021 season with the Double-A Tennessee Smokies and Triple-A Iowa Cubs.

On August 1, 2023, the Cubs traded Rodríguez, Adrian Sampson, and international free agent bonus pool space to the Tampa Bay Rays in exchange for Josh Roberson.

On November 6, 2023, the Rays added Rodríguez to their 40-man roster to prevent him from reaching minor league free agency.