Nowadays, generation of energy-tunable, monochromatic γ-rays is needed to establish a nondestructive assay method of nuclear fuel materials. The γ-rays are generated by collision of laser photons stored in a cavity and relativistic electrons. We propose a configuration of an enhancement cavity capable of performing polarization control fabricated by a combination of a four-mirror ring cavity with a small spot inside a cavity and a three-mirror of reflective optics as an image inverter for polarization-selectable γ-rays. The image inverter introduces a phase shift of specific polarization which can be used to generate an error signal to lock an optical cavity at a resonance condition.