Arc Synthetic Aperture Radar (Arc-SAR) is a new operation-mode radar that is suitable for wide observation in certain areas. With its high resolution, wide observation area, and short repetition visit period, Arc-SAR is widely used in monitoring deformation measurements, landslides, and natural hazards. Because of the special movement of Arc-SAR, the BackproPagation Algorithm (BPA) is widely used in its image processing. Here, we propose a novel two-dimensional frequency domain algorithm to process an Arc-SAR signal. First, we derive a signal model of Arc-SAR based on that of frequency-modulated continuous-wave radar. Next, because the length of the arm is far shorter than the distance of the antenna to the target, the signal can be processed in a 2D frequency domain. Finally, we analyze the error of the frequency method used. This algorithm has the advantages of high computation speed and accuracy. The simulation and experimental data results confirm the effectiveness and validity of the proposed method.