The closest he came to being a DJ was as a boyscout as a child. Cage had a radio program on KNX when he was 12, for the Boy Scouts of America. It began as a 30 minute program entirely comprised of performances by himself and other Boy scouts. Solo violin, solo piano piano and vocal. Strangely it's popularity led it to expand fo a 2-hour program. It was the kind of thing that was only possible in 1924. At the time KNX operated on 360 meters, and had only been granted those calls in May of 1922.
In 1982 he wrote a radio play "Marcel Duchamp, James Joyce, Erik Satie: An Alphabet" which was commissioned and performed on Westdeutscher Rundfunk WDR Radio in West Germany. It had 16 performers and one narrator and contained no music.
In 1966 Cage and Morton Feldman recorded four conversations billed as "Radio Happenings" at WBAI in New York. The series of sit downs ran from July 1966 and January 1967. There was no music, he composed nothing, they just rambled for half an hour or so each time.
CBS once commissioned a play group he worked with in Chicago to do a work based upon Kenneth Patchen's The City Wears a Slouch Hat. I can find no recording of it, but he does mention it in an interview here which I quote from below:
"My idea was to take a play, and thinking of the script as having ambient sounds to use those sounds, not as sound effects, but as the sounds of a music which would accompany the play. CBS liked that."But the most famous connection to radio is in performance. In 1955 he "wrote" a composition for 5 radios with two performers stationed at each radio. One is for tuning the radio-stations, the second is for adjusting the volume and tone. I put quotations around the word "wrote" because the content of the composition is inherently different at each performance even if the rhythm is the same. Below is the video form a 1982 performance of it.