Radiotherapy utilizes photons for treating cancer. Historically these photons have been produced by the bremsstrahlung process. In this paper we introduce Compton backscattering as an alternate method of photon production for cancer treatment. Compton backscattering is a well-established method to produce high-energy photons (gamma rays) for nuclear physics experiments. Compton backscattering involves the collision of a low-energy (eV) photon with a high-energy (hundreds of MeV) electron. It is shown that the photons scattered in the direction opposite to the direction of the initial photon (backscattered) will have the energy desired for photon beam therapy. The output of Compton backscattering is a high-energy photon beam (gamma-ray beam), which is well collimated and has minimal low-energy components. Such gamma beams may be used for conventional high-energy photon treatments, production of radionuclides, and generation of positrons and neutrons. The theoretical basis for this process is reviewed and Monte Carlo calculations of dose profiles for peak energies of 7, 15, and 30 MeV are presented. The potential advantages of the Compton process and its future role in radiotherapy will be discussed.