In 2011 Rodriguez originated the role of "Veronica" on Broadway in Stephen Adly Guirgis's play "The Motherfucker with the Hat". She was nominated for a Tony Award and won the Outer Critics Circle Award. The entire cast - Rodriguez, Bobby Cannavale, Chris Rock, Annabella Sciorra and Yul Vazquez - won the Theatre World Award for Best Ensemble.
She was born in Brooklyn, New York. She has been a close friend with actress Karina Ortiz.