Rodriguez surfaced in Venezuela in the late 1960's and early 1970's and was able to build a fan base there. He also participated in a famous commercial for Detergente Ace, along with his family during that time.
Rodriguez went to Puerto Rico, where he participated in Cristina Bazan along with Johanna Rosaly (no relation) and young Adamari Lopez. While there, he got his nickname, El Puma.
Later, he also made the soap opera El Idolo there, alongside Cuban actress Marylin Pupo.
Rodriguez's main money revenue, however, was his singing career. His hits included Dueno De Nada, Pavo Real and Agarrense De Las Manos. With Pavo Real, he caused a controversy at the 1982 contest of Miss Universe. The contest was being held in Atlanta, a Southern American state, and Pavo Real is a song about a mixed races matrimony. This didn't sit well with the organizers of the event.
Rodriguez was married until well into the 1980's with actress Lila Morillo, with whom he procreated 2 daughters. One of them, Liliana Morillo, is a famous actress in Venezuela now.
Rodriguez is a newborn christian, and he loves meeting his fans and signing autographs for them.
He relocated to Miami after his divorce from Morillo and soon found another romantic interest, with whom he has a daughter too.