This article introduces a method to provide a continuous one-way sweep of the axis modes in a Fabry-Pérot (FP) cavity without sweeping the cavity mirror. The concept is based on the geometrical phase for circularly polarized light. When a geometric phase shifter (GPS) composed of fixed and rotating phase plates is arranged within an FP cavity, the frequencies of the axis modes are controlled by the angle of the phase plate. Two types of GPS configuration are proposed and experimentally demonstrated, providing two tunable ranges of the axis modes per revolution (these being two or four times as wide as the free spectral range). Neighboring axis modes are connected by continuous rotation.