Torrini had begun drawing during the war, and afterwards earned a BFA at the St. Louis School of Fine Arts at Washington University, then was awarded a Fulbright scholarship to study for a year at the Accademia di Belle Arti di Firenze in Florence, Italy in 1949. Afterwards, he earned his MFA at the University of Notre Dame, where he studied under Ivan Meštrović. He went on to teach first at Webster College (now Webster University) for 17 years, then chaired the Art Department at Fontbonne College for 35 years.
