Semiconductor lasers (SLs) show relaxation oscillation (RO) due to the cavity damping rate being higher than the carrier damping rate. The presence of RO in SLs contributes to abundant complex dynamics when the laser is perturbed by external optical feedback (EOF). In this work, the influence of feedback optical phase on the relaxation oscillation frequency (ROF) in an SL is investigated both theoretically and experimentally. By numerically solving the well-known Lang Kobayashi equations, the relationship between the ROF and feedback optical phase was obtained, which shows ROF is in a sinusoidal manner with respect to the feedback optical phase under weak feedback strength. A simplified mathematic expression for ROF was derived to describe such a sinusoidal relationship. Potential sensing applications can be developed based on the relationship. As an example, a new method of measuring linewidth enhancement factor of an SL was presented. Finally, an experimental setup was built and experiments were carried out to verify the relationship and the measurement method for linewidth enhancement factor.