A novel concept for indoor self-localization based on relative position measurements to rotating artificial landmarks (with known positions) using short-range radar is proposed. This includes a complete processing pipeline for extracting distance and angle measurements from the raw radar data, which consists of a neural network for distance estimation, a basic angle-of-arrival estimator, and a particle filter for position tracking. Due to the ability of radar to measure range rate, i.e., the velocity in the direction of a detection, it is possible to robustly detect the landmarks by detecting and localizing their micro-Doppler pattern. This mean localization is possible even under difficult conditions (e.g., light changes). Experiments with a wheeled mobile robot and common office fans as landmarks demonstrate the effectiveness of the approach for indoor localization.