His international debut for Argentina on August 10, 1924 was against Uruguay. Over the next 12 years, he played 13 times for Argentina and scored 3 goals, winning the 1927 Copa América and the silver medal at the 1928 Summer Olympics in Amsterdam, Netherlands. Orsi's career is strange by modern standards, however, in that he played for Italy as well as Argentina, allowing him to gain 35 caps and score 13 goals for his second country between December 1, 1929 and March 24, 1935. This also allowed him to win two editions of the Central European International Cup, and to be a part of the side that won the 1934 FIFA World Cup, in the final of which he scored. He died in 1986 aged 84.