At the 2016 Summer Olympics, Rodríguez was selected to compete for Spain in both individual and team recurve tournaments. First, he led the Spanish trio by compiling a total of 1,986 points to finish eighth in the ranking round, along with his individual score of 678 as the tenth seed heading to the knockout stage. In the men's team recurve, Rodríguez and his compatriots Fernández and Alvariño bowed out to the Dutchmen in the opening round of the tournament, conceding a slick 1–5 defeat. Few days later, in the men's individual recurve, Rodríguez avenged his team's early exit by easily dispatching Malaysia's Muhammad Akmal Nor Hasrin and Belgium's Robin Ramaekers through the opening rounds, before he was disposed with a 3–7 score by Japanese archer and London 2012 silver medalist Takaharu Furukawa in his succeeding match.