He defected from Cuba at the same time as Vladimir Nunez.
Signed by the Diamondbacks as a free-agent in 1996, he began his professional career that very same year. A starter, he split time between the Lethbridge Black Diamonds and Visalia Oaks, going 9-6 with a 4.55 ERA. In 1997, he played for the South Bend Silver Hawks, going 4-11 with a 3.62 ERA. 1998 would end up being his final season. He played for both South Bend and the High Desert Mavericks, and he went a combined 0-4 with a 5.86 ERA in 43 innings of work.
Overall, Larry Rodriguez went 13-21 with a 4.40 ERA in 53 career games (46 starts). In 258 innings, he walked 72 and struck out 181.