Hyperbolic polaritons in extremely anisotropic materials have attracted intensive attention due to their exotic optical features. Recent advances in optical materials reveal unprecedented dispersion engineering of polaritons, resulting in twistronics for photons, canalized phonon polaritons, shear polaritons, and tunable topological polaritons. However, the on-demand reconfigurability of polaritons, especially with magnetic anisotropic dispersions, is restricted by weak natural magnetic anisotropy and hence remains largely unexplored. Here, we show how origami fused with artificial magnetism unveils a versatile pathway to topologically reconfigure magnetic polaritons. We experimentally demonstrate that the three-dimensional origami deformation allows to reconfigure hyperbolic or elliptic topology of polariton dispersion and modulate group velocity. With group velocity transitioning from positive to negative directions, we further report reconfigurable origami polariton circuitry in which the polariton propagation and phase distribution can be tailored. Our findings provide alternative perspectives on on-chip polaritonics, with potential applications in energy transfer, sensing, and information transport.