Righetti was born in 1916 in Rome.
He had his first exhibitions with figurative works in 1934. Righetti produced his first abstract works in 1937. He had many solo exihibitions in Italy and Paris with various art dealers and group exhibitions in the Salon des Réalités Nouvelles in Paris.
The French government granted Righetti scholarschips in 1947 and 1948. He also received diverse awards from the Italian goverment.
His work can be found in various collections and private collections in Naples, Milan, Rome, Paris, Amsterdam, Utrecht, Split, Buenos Aires and San Francisco.