The synthetic aperture radar (SAR) images of a moving target may be out of focus, given the motions of a non-cooperative target. Doppler ambiguities, including the Doppler center blur and spectrum ambiguity, will easily appear due to the limitations of pulse repetition frequency, which causes difficulty in moving-target imaging. Therefore, a robust fast Doppler ambiguity approach for SAR imaging of a ground-based moving target using range azimuth joint processing (RAJP) is presented. Firstly, the use of RAJP, based on a two-dimensional cross-correlation function and linear range cell migration (LRCM) compensation function, is proposed to simultaneously obtain the first- and second-order phase parameters in the fast-time and azimuth-frequency domains. Then, a corresponding azimuth reference function is constructed to image the moving target. Additionally, a principal component analysis-based operation is introduced to solve the mismatch with the LRCM compensation function. The couplings between the range and azimuth and between the first- and second-order parameters can be simultaneously decoupled by the proposed RAJP operation, which simplifies the processing steps. The developed approach can simultaneously obtain the first- and second-order parameters in the fast-time and azimuth-frequency domains, which avoids the propagation error of parameter estimation caused by the stepwise processing operation. The proposed method is relatively fast, given the need for fewer processing steps. The presented approach is robust in terms of Doppler ambiguity and handles the blind speed sidelobe well. In this study, simulated and real data are processed to verify the proposed approach.