He attended Brown University, receiving a degree in international relations in 2000, and, following his graduation, he joined the United States Peace Corps, serving in Senegal from 2000 to 2003 as a business advising volunteer. Upon returning to the country, Rodríguez attended Harvard Law School, graduating with his Juris Doctor in 2006, and then he moved back to Florida, where he taught as an adjunct clinical professor at the Carlos A. Costa Immigration & Human Rights Clinic at the Florida International University College of Law from 2008 to 2010 and then worked as an attorney for Florida Legal Services.
In 2012, following the reconfiguration of the state"s legislative districts Rodríguez opted to run in the newly-created 112th District. He faced Alex Dominguez in the Democratic primary, which the Miami Herald called a "low-key" race compared to the acidic Republican primary. Rodríguez was able to defeat Dominguez by a fairly wide margin, winning the primary with 58% of the vote and advancing to the general election, where he faced former State Senator Alex Díaz de la Portilla.
Against Díaz de la Portilla, Rodríguez campaigned on supporting public education, encouraging economic growth, and the fresh perspective that he would bring to the legislature, noting, "My opponent practically invented the business model of pandering to voters in Miami and then selling us out in Tallahassee." Ultimately, Rodríguez defeated Díaz de la Portilla by a relatively slim margin, receiving 54% of the vote to his opponent"s 46%.