Swank graduated with a Bachelor of Arts degree in physics from Bryn Mawr College in 1961. Two of her physics professors at Bryn Mawr were alumni of Caltech. They influenced her decision to attend graduate school at the California Institute of Technology. Under the supervision of Steve Frautschi, she was awarded her PhD in physics in 1967. Her thesis was "Radiative Corrections to Neutrino-Electron Interactions".
In 1971, Swank and her husband moved to Ankara, Turkey, to join the faculty of the Middle East Technical University as assistant professors. There she met Hakkı Boran Ögelman, a high-energy astrophysics researcher and head of the physics department at that time who had been involved in the gamma-ray astronomy group at the Goddard Space Flight Center. Through him, Swank learned of experiments under development for the eighth Orbiting Solar Observatory to be launched in 1975. After she returned to the United States, Swank applied for and received a postdoctoral fellowship at Goddard.