Righetti had his first exhibitions with figurative works in 1934. Righetti produced his first abstract works in 1937. He had many solo exhibitions in Italy and Paris with various art dealers and group exhibitions in the Salon des Réalités Nouvelles in Paris. The French government granted Righetti scholarships in 1947 and 1948. He also received diverse awards from the Italian government. His work can be found in various collections and private collections in Naples, Milan, Rome, Paris, Amsterdam, Utrecht, Split, Buenos Aires and San Francisco.