Synthetic Aperture Radar (SAR) utilizes the movement of the radar antenna over a specific area of interest to achieve higher spatial resolution imaging. In this paper, we aim to investigate the realization of SAR imaging for a stationary radar system with the assistance of active reconfigurable intelligent surface (ARIS) mounted on an unmanned aerial vehicle (UAV). As the UAV moves along the stationary trajectory, the ARIS can not only build a high-quality virtual line-of-sight (LoS) propagation path, but its mobility can also effectively create a much larger virtual aperture, which can be utilized to realize a SAR system. In this paper, we first present a range-Doppler (RD) imaging algorithm to obtain imaging results for the proposed ARIS-empowered SAR system. Then, to further improve the SAR imaging performance, we attempt to optimize the reflection coefficients of ARIS to maximize the signal-to-noise ratio (SNR) at the stationary radar receiver under the constraints of ARIS maximum power and amplification factor. An effective algorithm based on fractional programming (FP) and majorization minimization (MM) methods is developed to solve the resulting non-convex problem. Simulation results validate the effectiveness of ARIS-assisted SAR imaging and our proposed RD imaging and ARIS optimization algorithms.