Rodríguez rose to prominence in the international archery scene, when he and his compatriots Antonio Fernández and eventual individual champion Miguel Alvariño obtained a silver medal in the men's team recurve final against Ukraine at the 2015 European Games in Baku, Azerbaijan. He promptly followed the team archery results by helping the Spaniards secure a full quota spot for Rio 2016 at the World Championships few months later in Copenhagen, Denmark, booking his country's maiden appearance in an Olympic archery competition since 1992.