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 national team in preparation for the 2012 Summer Olympics. After the 2012 Olympics he returned to Léopold. Since 2015 he plays for Royal Beerschot. In March 2021 it was announced he would join Braxgata for the 2021–22 season.