This paper presents an angle-of-arrival (AOA) measurement system based on microwave photonic frequency down conversion. It has the novelty of no LO is needed for the frequency conversion process. Instead, a ramp waveform is used to shift the frequency of an optical carrier, which is phase modulated by a microwave signal in the subsequent stage. Two low-frequency IF signals are generated after photodetection. The AOA of the incoming microwave signal can be determined by measuring the phase difference of the two IF signals. Comparing with the previously reported frequency converter based AOA measurement systems, the proposed structure does not need a high-frequency tunable LO source and high-frequency electrical components. Expensive and bulky equipment such as an electrical spectrum analyser are not required in the proposed AOA measurement system. Experimental results show AOA measurement of different-frequency and different-power microwave signals, with small measurement errors.