A novel photonic approach for simultaneously measuring both the Doppler frequency shift (DFS) and the angle of arrival (AOA) of a microwave signal in a radar system is presented. It has the same structure as a fiber optic link consisting of a laser, an optical modulator and a photodetector. The incoming microwave signal and a reference signal are applied to the optical modulator. Beating of the echo and reference signal sidebands at the photodetector generates a low-frequency electrical signal. The DFS and the AOA can be determined from the frequency and the power of the low-frequency electrical signal measured on an electrical spectrum analyzer. The system has a very simple structure and is low-cost. It has a wide operating frequency range and a robust performance. Experimental results demonstrate a DFS measurement at around 15 GHz with errors of less than ±0.2 Hz, and a 0° to 90° AOA measurement with less than ±1° errors.