Synthetic aperture ladar (SAL) is a newly developed imaging device for remote sensing application. Owing to its short wavelength (3-5 orders of magnitude shorter than radar), SAL is very sensitive to platform vibration. For frequency-modulated continuous-wave SAL (FMCW-SAL), the platform vibration induces an additional range cell migration (RCM) to the SAL image. The vibration-induced RCM (VI-RCM) deteriorates the image quality. The VI-RCM is a unique problem for the FMCW-SAL imaging. To address this problem, a raw-data-driven method is proposed to correct the VI-RCM in this paper. First, the signal model was developed to show the VI-RCM in FMCW-SAL echo. Then, based on the model, the differential phase function (DPF) is constructed for the adjacent range profiles. The DPF is a single-frequency signal with its frequency being proportional to the relative range shift between the adjacent range profiles. Based on the DPF, the relative range shift is estimated. After the estimation of all the relative range shifts, the VI-RCM is calculated and corrected. Experiments are performed. The simulated experiment demonstrated the feasibility, accuracy, and efficiency of the proposed method, and the real data processing result verified the effectiveness of the proposed method for FMCW-SAL in practical applications.