The Finite Radon Transform (FRT) is a discrete analogue of classical tomography. The FRT permits exact reconstruction of a discrete object from its discrete projections. The set of projection angles for the FRT is intrinsic to each image array size. It is shown here that the set of FRT angles is closed under a rotation by any of its members. A periodic re-ordering of the elements of the 1D FRT projections is then equivalent to an exact 2D image rotation. FRT-based rotations require minimal interpolation and preserve all of the original image pixel intensities. This approach has applications in image feature matching, multi-scale data representation and data encryption.