After receiving his PhD, Corson spent the next two years as a post-doctoral fellow in the Radiation Laboratory at the University of California, Berkeley to help construct a 60-inch cyclotron. In 1939, Emilio Segrè suggested that the cyclotron could be used to bombard bismuth (element 83) with alpha particles to produce the then-unknown element 85. Corson, Kenneth Ross MacKenzie, and Segrè discovered and isolated the element in 1940. They named it "astatine" in 1947.
In 1946 Corson came to Cornell University as an assistant professor of physics and helped design the Cornell synchrotron. He was appointed associate professor of physics in 1947, became a full professor in 1956, was named chairman of the physics department in 1956, and became dean of the College of Engineering in 1959. Following the 1969 resignation of James A. Perkins, Corson became president of Cornell and served until 1977 after which he served for three years as chancellor. In 1979, he was elected by the Board of Trustees as president emeritus.