Voicu was born in Bucharest, into a family of professional musicians. At age 6, he had his first music lessons with Constantin Niculescu. At age 14, he entered the Royal Academy of Music in Bucharest, where he studied with George Enocovici. After graduating in 1940, he became violinist with the National Radio Orchestra of Romania, where he was noticed by the conductor, Willem Mengelberg; Voicu made his debut as a soloist with the orchestra soon after. In 1946, he won the first prize at a musical competition organized in Bucharest by George Enescu and Yehudi Menuhin.