Fodor was born in Denver, Colorado. His first ten years of study were with Harold Wippler, who taught him from 1958 until 1968. Wippler observed that "It was very apparent that he had exceptional talent. Not just technical talent but a great, unusual understanding of music". He then studied at the Juilliard School in New York City, Indiana University and the University of Southern California, where his teachers included Ivan Galamian, Josef Gingold and Jascha Heifetz, respectively.
Fodor made his solo debut with the Denver Symphony at the age of ten, playing Max Bruch's Violin Concerto No. 1, and began touring as a soloist while still a young teenager.
Fodor won numerous national contests before the age of seventeen, including First Prize in both the Merriweather Post Competition in Washington, D.C. and the Young Musicians Foundation Competition in Los Angeles, California.
He went on to win first prize in the Paganini Competition in Italy in 1972, at the age of 22. It was this win that gained him widespread public attention. He achieved the highest prize awarded (second prize, shared with two other violinists) in the International Tchaikovsky Competition in 1974 in Moscow, Russia. This award raised his profile further, as an American sharing the top Soviet prize during the height of the Cold War. He signed a recording contract with RCA Red Seal and was a frequent guest on The Tonight Show Starring Johnny Carson. Fodor was also awarded the European Soloist award "Prix Europeen du Soliste" in January 1999.
He appeared on the television show SCTV on 20 November 1981 in a parody of the Joan Crawford movie Humoresque called New York Rhapsody.
His career declined in the late 1980s after an arrest for drug possession on Martha's Vineyard in 1989 resulted in negative publicity.
He died from cirrhosis in Arlington County, Virginia, at the age of 60. His first marriage was to Susan Davis in 1978 and they divorced in 1986. His second marriage to Sally Svetland also ended in divorce. He remarried Susan in November 2010. He and Susan had three children and two grandchildren.