Magnetization switching by current-induced spin-orbit torques is of great interest due to its potential applications in ultralow-power memory and logic devices. The switching of ferromagnets with perpendicular magnetization is of particular technological relevance. However, in such materials, the presence of an in-plane external magnetic field is typically required to assist spin-orbit torque-driven switching and this is an obstacle for practical applications. Here, we report the switching of out-of-plane magnetized Ta/Co(20)Fe(60)B(20)/TaO(x) structures by spin-orbit torques driven by in-plane currents, without the need for any external magnetic fields. This is achieved by introducing a lateral structural asymmetry into our devices, which gives rise to a new field-like spin-orbit torque when in-plane current flows in these structures. The direction of the current-induced effective field corresponding to this field-like spin-orbit torque is out-of-plane, facilitating the switching of perpendicular magnets.