We present a deep learning-based approach called DipSAR for reconstructing millimeter-wave synthetic aperture radar (SAR) images from sparse samples. The primary challenge lies in the requirement of a large training dataset for deep learning schemes. To overcome this issue, we employ the deep image prior (DIP) technique, which eliminates the need for a large dataset and instead utilizes only the sparse sample itself. Our proposed DipSAR model recovers missing samples from sparse data and reconstructs the SAR image using a conventional method. In this study, we utilize an existing SAR dataset and create fourteen different patterns to generate additional sparse samples by removing certain data points. We then evaluate the performance of DipSAR in comparison to the conventional method. The results show that DipSAR outperforms the conventional method in terms of the intersection over union (IoU) score.