Most of the existing research on the dynamics of magnetic solitons such as a domain wall (DW) has focused on the effect of DC forces, where the induced velocity is determined by the force strength. Here we show that AC forces such as an oscillating magnetic field or current are also able to move a DW straight via synchronization between the DW angle and the phase of the AC force. The resulting DW velocity is solely proportional to the driving frequency of the AC force, but the strength of the AC field just affects the frequency range for criteria for the phase-locking behavior. The AC-force-driven DW motion is shown to exhibit a phase locking-unlocking transition, a critical phenomenon akin to the Walker breakdown of a DC-bias-driven DW motion. Our work shows that a DW can be driven straight by synchronizing its angle to AC forces and thereby demonstrates a proof-of-concept of magnetic soliton rectifiers (i.e., DC motion induced by AC forces), shedding a light on the hitherto overlooked utility of internal degree of freedom for driving magnetic textures.