A novel, to the best of our knowledge, photonics-assisted approach for measuring the angle-of-arrival (AOA) of microwave signals with a large measurement range is proposed. The system utilizes a dual-drive Mach-Zehnder modulator (DDMZM) for signal modulation, followed by an optical filter for sideband selection. The dc port of the DDMZM is fed by a triangular wave to generate a pair of opposite frequency shifts. An intermediate frequency (IF) signal with a periodic phase jump is obtained after photodetection. The AOA of the incoming signals can be estimated by measuring the value of the phase jump. The key novelty of the proposed scheme lies in the application of a triangular wave to shift the frequency of optical signals, which introduces a periodic phase jump to the IF signal. The system incorporates only a single optical channel, largely reducing the system complexity. Experimental results show that an AOA measurement with a range of -70.8° to 70.8° is realized, with errors confined to within ±2°.