In this paper, we propose and experimentally verify a phase-modulated radio-over-fiber (RoF) link capable of transmitting the radio frequency (RF) signal linearly. By executing the Kramers-Kronig (KK) algorithm at the receiver, the proposed link can accomplish linear optical phase demodulation with a single photodetector rather than a coherent receiver. In the 16-quadrature amplitude modulation (16-QAM) and 64-QAM microwave vector signal transmission experiments, measured error vector magnitudes (EVMs) are 4.14% and 4.38%, respectively, after 25-km fiber transmission, and the measured spurious-free dynamic range (SFDR) is 114.5 dB·Hz2/3, which shows a good performance in linearity.