Carrà was born on 18 June 1943 in Bologna to Raffaele Pelloni and Angela Iris Dell'Utri (of Sicilian ancestry) and had a brother named Enzo (died 2001). Her parents, however, separated shortly after the wedding and Carrà spent most of her childhood between her mother's bar and the ice cream shop in Bellaria – Igea Marina. At the latter establishment, she grew up watching the television programme Il Musichiere, learning by heart titles, ballets, and refrains of the songs.
When she was only eight years old, she left the Romagna Riviera to continue her studies directly in Rome at the National Academy of Dance. At the age of 14 she dropped out of ballet classes. In 1952 she began her studies at the Centro Sperimentale di Cinematografia until she graduated in 1960.