We theoretically study a ferrimagnetic domain-wall motion driven by a rotating magnetic field. We find that, depending on the magnitude and the frequency of the rotating field, the dynamics of a ferrimagnetic domain wall can be classified into two regimes. First, when the frequency is lower than a certain critical frequency set by the field magnitude, there is a stationary solution for the domain-wall dynamics, where a domain-wall in-plane magnetization rotates in-phase with the external field. The field-induced precession of the domain wall gives rise to the translational motion of the domain wall via the gyrotropic coupling between the domain-wall angle and position. In this so-called phase-locking regime, a domain-wall velocity increases as the frequency increases. Second, when the frequency exceeds the critical frequency, a domain-wall angle precession is not synchronous with the applied field. In this phase-unlocking regime, a domain-wall velocity decreases as the frequency increases. Moreover, the direction of the domain-wall motion is found to be reversed across the angular compensation point where the net spin density of the ferrimagnet changes its sign. Our work suggests that the dynamics of magnetic solitons under time-varying biases may serve as platform to study critical phenomena.