Cigna was born in Paris, France, to parents of Italian origin. She trained as a pianist at the Paris Conservatory studying with Alfred Cortot and graduated with a gold medal. She then started a career as a recitalist. She met French tenor Maurice Sens, whom she married in 1923, and following his advice turned to singing. She took private lessons with Emma Calvé, Hariclea Darclée and Rosina Storchio, but was mostly self-taught. She made her debut as Ginette Sens in 1927 at the Teatro alla Scala, in Milan, as Freia in Das Rheingold, without much success.
Two years later, still at La Scala, but this time under the name Gina Cigna, she sang the role of Donna Elvira in Don Giovanni, and this time it was a triumph. A few weeks later she appeared as Elisabeth in Tannhäuser. She was to sing regularly at La Scala until 1945, quickly establishing herself as one of the leading Italian dramatic soprano alongside Maria Caniglia in operas such as Il Trovatore, Un ballo in maschera, La forza del destino, Aida, Andrea Chénier, and Tosca. However, it is as Norma, La Gioconda and Turandot that her name will remain forever associated. She recorded Norma in 1937 and Turandot, opposite Francesco Merli, with the young Magda Olivero as Liù, in 1938, both for Cetra Records. As the first complete recordings of these two operas, they are both of considerable historical value.
As her reputation grew invitations from abroad started to materialize, and she sang at the Paris Opéra, the Royal Opera House in London, the Lyric Opera of Chicago, the San Francisco Opera, and the New York Metropolitan Opera, where she made her debut on February 6, 1937 as Aida.
Cigna's career came to a brutal halt in 1948 when she was involved in a serious car accident and suffered a heart attack. Forced to retire from singing, she turned to teaching. Amongst her pupils were Ghena Dimitrova, Luis Lima and Elena Mauti Nunziata. In 1996 at the age of 96 she appeared in Jan Schmidt-Garre's film Opera Fanatic.
She died in Milan, Italy, on June 20, 2001, at the age of 101.