Rossi played for Banco Provincia in Argentina. During the 2005–06 season, he played for Harvestehude in the German Bundesliga. He returned to Europe for the 2007–08 season when he signed for Orée in Belgium. He left Orée in 2010 for Léopold. After one season at Léopold he returned to Argentina to focus on the nationalteam in preparation for the Field hockey at the [2012 Summer Olympics – Men's tournament|2012 Summer Olympics]. After the 2012 Olympics he returned to Léopold. Since 2015 he played for Royal Beerschot. It was announced in March 2021 that he would join Braxgata for the 2021–22 season. After two seasons at Braxgata he returned to Beerschot as they play in the Belgian second division.