Interest in radial MRI (also known as projection reconstruction (PR) MRI) has increased recently for uses such as fast scanning and undersampled acquisitions. Additionally, PR acquisitions offer intrinsic advantages over standard two-dimensional Fourier transform (2DFT) imaging with respect to motion of the imaged object. It is well known that aligning each spatial domain projection's center of mass (calculated using the 0th and 1st moments) to the center of the field of view (FOV) corrects shifts caused by in-plane translation. In this work, a previously unrealized ability to determine the in-plane rotational motion of an imaged object using the 2nd moments of the spatial domain projections in conjunction with a specific projection angle acquisition time order is reported. We performed the correction using only the PR data itself acquired with the newly proposed projection angle acquisition time order. With the proposed view angle acquisition order, the acquisition is "self-navigating" with respect to both in-plane translation and rotation. We reconstructed the images using the aligned projections and detected acquisition angles to significantly reduce image artifacts due to such motion. The theory of the correction technique is described, and its effectiveness is demonstrated in phantom and in vivo experiments.