The methods of computerized tomography (CT), developed for medical X-ray applications, can be adapted for use in studying plasma X-ray emissivity distributions in tokamaks and other magnetic confinement devices. The authors demonstrate the feasibility of the technique by reconstructing test patterns with data simulated for a number of different types of detector arrangements. They also use the technique with real data to reconstruct a rotating emissivity feature on a cross section of Massachusetts Institute of Technology's Alcator A tokamak.