Rodríguez celebrated his greatest successes with two tournament wins in doubles in 1968 and 1969. In 1973 he reached 133rd place, the best position of his career in the world singles rankings. The last time he was on December 31, 1978 with place 496 in the individual world rankings of men.
He played from 1958 in a total of 20 matches for the Chilean Davis Cup team and has a total of 19:25, of which 18:17 in singles and 1: 8 in doubles.