Cox was elected to the United States National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society. In 1969 the American Geophysical Union awarded him the John Adam Fleming medal for research in geomagnetism ;. In 1970 he was awarded the prestigious Vetlesen Prize, along with G. Brent Dalrymple, Richard Doell and S. Keith Runcorn, for contributions to geology and geophysics. In 1976 the Geological Society of America awarded him the Arthur L. Day Medal for the application of physics and chemistry to the solution of geologic problems. He was the president of the American Geophysical Union from 1978 to 1980. In 1984 the United States National Academy of Sciences awarded him the Arthur L. Day Prize and Lectureship.