Radio frequency identification (RFID) technology has become increasingly important in intelligent warehouse management and logistics tracking systems. However, conventional commercial RFID systems, operating within the Industrial, Scientific, and medical radio band, are constrained by limited bandwidth, which hinders high-precision carrier phase-based ranging. Moreover, in scenarios such as mobile robots and handheld readers, the deployment of multi-antenna arrays is impractical due to space limitations, posing further challenges to angle-based localization techniques. To address these issues, this paper proposes a synthetic aperture-based RFID localization system utilizing a single antenna and a single-frequency point. The system constructs a spatially non-uniform virtual linear array by collecting phase sequences and corresponding timestamps during antenna motion. A fast coarse angle estimation algorithm based on the derivative of the phase sequence is introduced to reduce the search space and improve estimation efficiency. Furthermore, the phase differences between distinct virtual antenna positions are used to compute differential distances to the target tag. These distance differences, combined with angle information, are formulated into a hyperbolic localization model. The final coordinates of the RFID tag are estimated using a particle swarm optimization algorithm with adaptive weighting. Experimental results validate the effectiveness of the proposed system, the median error of differential distance estimation is 4.2 cm, the median angle estimation error is 1°, and the final localization median error reaches 3.45 cm. The proposed method achieves highaccuracy localization on commercial RFID platforms without additional hardware costs, and thus holds promising practical application value.