Magnetization switching by current-induced spin-orbit torques (SOTs) is of great interest due to its potential applications for ultralow-power memory and logic devices. In order to be of technological interest, SOT effects need to switch ferromagnets with a perpendicular (out-of-plane) magnetization. Currently, however, this typically requires the presence of an in-plane external magnetic field, which is a major obstacle for practical applications. Here we report for the first time on SOT-induced switching of out-of-plane magnetized Ta/Co20Fe60B20/TaOx structures without the need for any external magnetic fields, driven by in-plane currents. This is achieved by introducing a lateral structural asymmetry into our devices during fabrication. The results show that a new field-like SOT is induced by in-plane currents in such asymmetric structures. The direction of the current-induced effective field corresponding to this new field-like SOT is out-of-plane, which facilitates switching of perpendicular magnets. This work thus provides a pathway towards bias-field-free SOT devices.