Radar-based object detection is essential for autonomous driving due to radar's long detection range. However, the sparsity of radar point clouds, especially at long range, poses challenges for accurate detection. Existing methods increase point density through temporal aggregation with ego-motion compensation, but this approach introduces scatter from dynamic objects, degrading detection performance. We propose DoppDrive, a novel Doppler-Driven temporal aggregation method that enhances radar point cloud density while minimizing scatter. Points from previous frames are shifted radially according to their dynamic Doppler component to eliminate radial scatter, with each point assigned a unique aggregation duration based on its Doppler and angle to minimize tangential scatter. DoppDrive is a point cloud density enhancement step applied before detection, compatible with any detector, and we demonstrate that it significantly improves object detection performance across various detectors and datasets.