The 4D millimeter wave radar has gained increasing attention in autonomous driving due to its robustness against environmental interference compared to other perception devices such as cameras or LiDAR. However, the practical deployment of radar remains challenging due to the noise and high sparsity of radar point clouds, as well as the resource limitations of edge computing. To address these issues, we propose Radar-Mamba, a lightweight and efficient radar enhancement approach for boosting radar perception. The proposed approach contains three main components: cross-modal alignment, radar enhancement architecture based on the Mamba model, and Doppler feature fusion. Specifically, the point clouds of radar and LiDAR are first refined and aligned to build more dense and rich occupancies. The aligned 4D radar data is then enhanced by capturing both local and global spatial-temporal features, while integrating radar-specific velocity and elevation information for further denoising. Experiments on two open-source datasets demonstrate that our method achieves state-of-the-art performance and generates high-quality 4D point clouds with a density comparable to LiDAR while maintaining a low parameter count friendly for practical deployment.