We present a new method for rigid registration of CT scans in Radon space. The inputs are the two 3D Radon transforms of the CT scans, one densely sampled and the other sparsely sampled. The output is the rigid transformation that best matches them. The algorithm starts by finding the best matching between each direction vector in the sparse transform and the corresponding direction vector in the dense transform. It then solves the system of linear equations derived from the direction vector pairs. Our method can be used to register two CT scans and to register a baseline scan to the patient with reduced-dose scanning without compromising registration accuracy. Our preliminary simulation results on the Shepp-Logan head phantom dataset and a pair of clinical head CT scans indicates that our 3D Radon space rigid registration method performs significantly better than image-based registration for very few scan angles and comparably for densely-sampled scans.