The recently developed rotating radiofrequency coil (RRFC) technique has been proven to be an alternative solution to phased-array coils for magnetic resonance imaging (MRI). However, most of the image reconstruction methods for the RRFC requires detailed knowledge of coil sensitivity to yield optimal results. In this work, a novel reconstruction algorithm based on Robust Principal Component Analysis (RPCA) with the k-t (k-space-time domain) sparse bin reformation method (or rotating k-t bin method) has been presented to restore images without using dedicated coil sensitivity information. The proposed algorithm recovers images by iteratively removing the artefacts in both temporal and frequency domains caused by the Fourier invariant violation from coil rotation. The data sampling scheme consists of the golden angle (GA) radial k-space and the stepping-mode coil rotation. Simulation results demonstrate the effectiveness of the proposed imaging method for the RRFC-based MR scan.