We demonstrate a novel photonic radio frequency (RF) phase shifter/modulator based on dispersion-induced optical quadrature double-sideband modulation (OQDSB) and differential detection. An optical phase modulator cascaded with a dispersive element is used to implement OQDSB. The OQDSB signal then passes through a dual-output phase-tunable Mazh-Zehnder interferometer, and the two outputs are differentially detected. A full 360°-tuning range is experimentally demonstrated at 14 GHz. The bandwidth in which the amplitude variation is less than 1 dB is 660 MHz, and the bandwidth in which the nonlinear phase variation is less than 5° is 520 MHz.