Rodríguez was born in Santa Cruz de Tenerife, Canary Islands, Spain. He started his professional career with CB Tenerife of the Spanish second-tier level LEB Oro in 1997. In 2001, he moved to the top-flight Liga ACB with CB Estudiantes. He played three seasons with Estudiantes before moving to Real Madrid in 2004. He played with Real Madrid for two seasons before moving to the NBA in 2006.
Rodríguez was drafted 52nd overall in the 2001 NBA draft by the Phoenix Suns, but he did not sign with the team. He finally made it to the NBA in 2006, signing a two-year contract with the New Orleans Hornets. He played one season with the Hornets before being traded to the Philadelphia 76ers. He played three seasons with the 76ers before being traded to the Sacramento Kings in 2010. He played two seasons with the Kings before being waived in 2012.
Rodríguez returned to Europe in 2012, signing with Fenerbahçe Ülker of the Turkish Basketball League. He played two seasons with Fenerbahçe before moving to Unicaja Málaga in 2014. He played one season with Unicaja before returning to CB Tenerife in 2015. He played one season with Tenerife before retiring from professional basketball in 2016.
Rodríguez represented the Spanish national basketball team at the 2004 Summer Olympics, the 2006 FIBA World Championship, and the 2007 FIBA EuroBasket. He won the bronze medal at the 2004 Olympics and the silver medal at the 2006 World Championship.
