Rodriguez's Broadway credits include The Addams FamilyIn the Heights, Spring Awakening, and A Chorus Line.
Additionally, it has been announced that Leslie Odom, Jr. will join the series full time. He guest-starred during the first season as Sam, the boyfriend of Christian Borle's character, songwriter Tom Levitt.
As previously reported, Jeremy Jordan and Andy Mientus will also join the cast of drama, along with Academy Award-winner Jennifer Hudson, who will make a multi-episode guest appearance.
Smash, which focuses on the making of a Broadway musical, also stars Debra Messing, Jack Davenport, Megan Hilty, and Anjelica Huston.