Recently, the concept of core-anti-resonant reflection (CARR) has been proposed, greatly expanding the options of cladding materials and morphologies for Fabry-Perot-type (F-P) cavities. For instance, a single-layer tube made of A4 paper can be a precision resonator in the terahertz (THz) band, which seemed counterintuitive before. More importantly, thanks to the involvement of paper-like materials as the cavity plates, it is possible to equip the CARR cavity with the currently popular origami functionality. Following this clue, in this work we combined a simple octagonal paper tube with different origami patterns and realized the programmable adjustment for the distance between two parallel surfaces of the tubular cavity. Accordingly, the combination of the CARR cavity and the origami property offers a new degree of freedom and flexibility to vary the cavity distance, tune the resonant frequency, and explore related applications. For applied examples, we carried out pressure sensing with this foldable structure and achieved a high sensitivity (S = 57.9 kPa-1). Meanwhile, the origami cavity could also act as a THz polarization converter, and the output polarization state of the cavity mode was easily modulated from the original linear to circular polarizations with different chiralities. In future works, besides the pressure-driven method used here, heat and magnetism, etc., can further be employed to tune the CARR cavity, benefiting from four dimensional (4D) or soft-magneto origami materials as the cavity wall.