Perpendicular synthetic antiferromagnets (p-SAFs) are of interest for the next generation of ultrafast, high-density spintronic memory and logic devices. However, to efficiently operate their magnetic order by current-induced spin-orbit torques (SOTs), an unfavored high external magnetic field is conventionally required to break the symmetry. Here, we report the field-free SOT switching of a p-SAF through the introduction of an interlayerwith Dzyaloshinskii-Moriya interactions (DMIs). We experimentally observe the existence of the DMI interlayer in our SAF sample by an azimuthal angular-dependent anomalous Hall measurement. Deterministic field-free switching is accomplished in such a sample and depicted by macrospin and micromagnetic simulations. The comparison between the uniaxial interlayer DMI and the azimuthal direction-dependent switching behavior strongly suggests its origin from the DMI interlayer. We demonstrate the compatibility of the proposed strategy with magnetic tunnel junction device structure. Our results provide a strategy for p-SAF-based high-performance SOT devices.