Autoresonance is a self-sustained resonance mechanism due to a driving force whose frequency monotonically varies with time. We theoretically show that the autoresonance mechanism allows an efficient switching of perpendicular magnetization by spin-orbit spin-transfer torques. We find that a threshold current for the autoresonant switching can be much smaller than that of conventional spin-orbit torque switching driven by a DC current. Moreover, the suggested scheme allows fully deterministic switching without the help of any external field.