In this paper, we propose a method for reconstructing synthetic aperture radar (SAR) images by applying a compressive sensing (CS) technique to sparsely acquired radar sensor data. In general, SAR image reconstruction algorithms require radar sensor data acquired at regular spatial intervals. However, when the speed of the radar-equipped platform is not constant, it is difficult to consistently perform regular data acquisitions. Therefore, we used the CS-based signal recovery method to efficiently reconstruct SAR images even when regular data acquisition was not performed. In the proposed method, we used the l1-norm minimization to overcome the non-uniform data acquisition problem, which replaced the Fourier transform and inverse Fourier transform in the conventional SAR image reconstruction method. In addition, to reduce the phase distortion of the recovered signal, the proposed method was applied to each of the in-phase and quadrature components of the acquired radar sensor data. To evaluate the performance of the proposed method, we conducted experiments using an automotive frequency-modulated continuous wave radar sensor. Then, the quality of the SAR image reconstructed with data acquired at regular intervals was compared with the quality of images reconstructed with data acquired at non-uniform intervals. Using the proposed method, even if only 70% of the regularly acquired radar sensor data was used, a SAR image having a correlation of 0.83 could be reconstructed.