Jordan was born Irving Sidney Jordan in New York City in April 1922. He studied classical music as a teenager and played in swing-era bands.
He was known for his pioneering work with saxophonist Charlie Parker. He played in Parker's quintet from 1946-1948 alongside trumpeter Miles Davis, drummer Max Roach and bass player Tommy Potter, recording classics like Embraceable You, Crazeology and Scrapple from the Apple on the Savoy and Dial Records labels.
Jordan left Parker's band in the autumn of 1948 and played with saxophonists Sonny Stitt, Gene Ammons, Stan Getz and Coleman Hawkins. He led his own quartet and created the jazz classic Jor-du; he also wrote part of the soundtrack of the 1959 Roger Vadim film Les Liaisons Dangereuses.
Jordan, an African American, married white jazz singer Sheila Jordan in 1952, when interracial marriages were almost nonexistent. The couple divorced a few years later. JazzTimes writes that Jordan had developed a heroin habit by the mid-1960s, but rehabilitated himself in the 1970s and re-started his music career in Copenhagen.
After the 1970s, Jordan worked mainly in Europe and recorded prolifically for the SteepleChase label.
He died in Valby, a suburb of Copenhagen, where he had lived since 1978.