N'ọnwa Ọgọstụ 2006, Rodríguez meriri nrite ọla edo na 2006 FIBA World Championship, mgbe ọ na-egwu egwuregwu na ndị okenye nke ndị otu mba Spain. O ritere ọlaọcha na ndị otu egwuregwu mba Spain na EuroBasket 2007. N'afọ 2012, o ritere ọlaọcha n'egwuregwu Olimpik n'obodo London. N'afọ 2016, o ritere ọla nchara n'egwuregwu Olimpik
na Rio de Janeiro.