The frequency-modulated continuous-wave (FMCW) synthetic aperture radar (SAR) is a light-weight,cost-effective, high-resolution imaging radar, which is suitable for a small flight platform. The signal model is derived for FMCW SAR used in unmanned aerial vehicles (UAV) reconnaissance and remote sensing. An appropriate algorithm is proposed. The algorithm performs the range cell migration correction (RCMC) for continuous nonchirped raw data using the energy invariance of the scaling of a signal in the scale domain. The azimuth processing is based on step transform without geometric resampling operation. The complete derivation of the algorithm is presented. The algorithm performance is shown by simulation results.