Spin-orbit torque (SOT)-induced magnetization switching shows promise for realizing ultrafast and reliable spintronics devices. Bipolar switching of perpendicular magnetization via 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 FM. In this material system, thanks to the exchange-bias effect of the AFM, we observe the switching under no 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 by 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.