We propose to use a parametric mixer in a passive phase correction scheme for stable distribution of a millimeter-wave signal over fiber links. The parametric mixer is realized via ultrafast four-wave mixing processes, thereby overcoming the bandwidth limit of conventional electronic devices. The mixing of round-trip probe and local pumps generates a signal immune to transmission delay fluctuations at the remote end. This scheme is validated by an experiment that distributes a 36-GHz millimeter wave over 20-km optical fiber. The remote frequency stability achieves 4.0×10-16 at 2000 s, indicating that this approach is promising for phase-stabilized delivery of high-frequency signals.