Spin-orbit torque (SOT)-induced magnetization switching shows promise for realizing ultrafast and reliable spintronics devices. Bipolar switching of the perpendicular magnetization by the SOT is achieved under an in-plane magnetic field collinear with an applied current. Typical structures studied so far comprise a nonmagnet/ferromagnet (NM/FM) bilayer, where the spin Hall effect in the NM is responsible for the switching. Here we show that an antiferromagnet/ferromagnet (AFM/FM) bilayer system also exhibits a SOT large enough to switch the magnetization of the FM. In this material system, thanks to the exchange bias of the AFM, we observe the switching in the absence of an applied field by using an antiferromagnetic PtMn and ferromagnetic Co/Ni multilayer with a perpendicular easy axis. Furthermore, tailoring the stack achieves a memristor-like behaviour where a portion of the reversed magnetization can be controlled in an analogue manner. The AFM/FM system is thus a promising building block for SOT devices as well as providing an attractive pathway towards neuromorphic computing.