At the 2012 Summer Olympics, Rossi competed for the national team in the men's tournament. He was a part of the Argentina squad which won the gold medal at the 2016 Summer Olympics. Rossi has won the bronze medal at the 2014 Men's Hockey World Cup and two gold medals at the Pan American Games. He retired from international hockey after the 2018 World Cup to spend more time with his family. In October 2019, he returned in the national team as he was called up for the October 2019 Europe tour.