Ralf was born in Malmö. He began his vocal studies in Stockholm with Haldis Ingebjart and John Forsell, and later studied in Berlin with Hertha Dehmlow. He made his debut in 1930, as Cavaradossi in Stettin. After singing in Chemnitz (1931–33) and Frankfurt (1933–35), he joined the Staatsoper Dresden in 1935. He also appeared regularly at the Munich State Opera and the Vienna State Opera, establishing himself in roles such as Florestan, Tannhäuser, Lohengrin, Stolzing, Siegmund, Tristan, Parsifal, Bacchus, but also Radames, Otello.
Ralf made guest appearances at the Royal Opera House in London, the Teatro Colón in Buenos Aires. During the war, Ralf sang with the Berlin State Opera and the Stockholm Opera. He made his debut at the New York Metropolitan Opera in 1945, as Lohengrin under the baton of Fritz Busch, he sang at the Met for three seasons.
In 1952 he received the title of Court Opera Singer in Sweden. Ralf died unexpectedly in Stockholm in 1954, but several recordings survive, notably his excerpts of Lohengrin with Tiana Lemnitz as Elsa, Tristan with Helen Traubel as Isolde, as well as scenes from Die Frau ohne Schatten with Hilde Konetzni.
- Verdi – Otello – Torsten Ralf, Hilde Konetzni, Paul Schoffler – Vienna State Opera Chorus and Orchestra, Karl Böhm – Cantus Classic (complete recording sung in German, 1944)
- Wagner "Die Meistersinger" Act III, Torsten Ralf, Margarete Teschemacher, Hans Hermann Nissen, others, Dresden Staatsoper Chorus and Staatskapelle Dresden [(Karl Böhm)] in German (1938) on Hänssler Profil.
- Wagner "Die Walkure". With Helene Werth, and Gertrude Grob-Prandl, with Robert F. Denzler conducting the orchestra of La Suisse Romande.