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. Current generation CT scanners reconstruct maps of x-ray absorptivity on body cross sections by processing transmission data from a number of fan-shaped beams of x rays. Analogous fan beam emission data can be obtained from confined plasmas by collimating emitted soft x rays with a "pin hole" or slit and detecting them with a linear array of solid-state detectors. Data from a number of such one-dimensional views of the plasma can be used to reconstruct a two-dimensional "photograph" of the absolute x-ray emission in cross section. No a priori assumptions about the nature of the emissivity distribution are necessary. In this paper we demonstrate the feasibility of the technique by reconstructing test patterns with data simulated for a number of different types of detector arrangements. We 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.