Exchange bias, a shift in the hysteresis loop of a ferromagnet arising from interfacial exchange coupling between adjacent ferromagnetic and antiferromagnetic layers, is an integral part of spintronic devices. Here, we show that spin-orbit torque generated from spin current, a promising approach to switch the ferromagnetic magnetization of next-generation magnetic random access memory, can also be used to manipulate the exchange bias. Applying current pulses to a Pt/Co/IrMn trilayer causes concurrent switching of ferromagnetic magnetization and exchange bias, but with different underlying mechanisms. This implies that the ferromagnetic magnetization and exchange bias can be manipulated independently. Our work demonstrates that spin-orbit torque in ferromagnet/antiferromagnet heterostructures facilitates independent manipulations of distinct magnetic properties, motivating innovative designs for future spintronics devices.