Applications of aerial robots are progressively expanding into complex urban and natural environments. Despite remarkable advancements in the field, robotic rotorcraft is still drastically limited by the environment in which they operate. Obstacle detection and avoidance systems have functionality limitations and substantially add to the computational complexity of the onboard equipment of flying vehicles. Furthermore, they often cannot identify difficult-to-detect obstacles such as windows and wires. Robustness to physical contact with the environment is essential to mitigate these limitations and continue mission completion. However, many current mechanical impact protection concepts are either not sufficiently effective or too heavy and cumbersome, severely limiting the flight time and the capability of flying in constrained and narrow spaces. Therefore, novel impact protection systems are needed to enable flying robots to navigate in confined or heavily cluttered environments easily, safely, and efficiently while minimizing the performance penalty caused by the protection method. Here, we report the development of a protection system for robotic rotorcraft consisting of a free-to-spin circular protector that is able to decouple impact yawing moments from the vehicle, combined with a cyclic origami impact cushion capable of reducing the peak impact force experienced by the vehicle. Experimental results using a sensor-equipped miniature quadrotor demonstrated the impact resilience effectiveness of the Rotary Origami Protective System (Rotorigami) for a variety of collision scenarios. We anticipate this work to be a starting point for the exploitation of origami structures in the passive or active impact protection of robotic vehicles.