The work presented in this paper demonstrates, for the first time, the combination of Origami-based solutions with wireless power transfer for the wireless charging of UAVs. The proposed lightweight, compact, yet large aperture structure is capable of delivering high efficiency power transfer links at relatively long ranges. The design features an Origami Starshade-inspired 28 MHz coil design fabricated on a sheet of paper using copper tape. The coil can be folded yielding at least 85% area reduction compared to its unfolded counterpart. This compactness allows the UAV to fly freely carrying a large yet compact and lightweight coil. For charging purposes, the receiving coil unfolds to match the size of the transmitting coil, enabling the delivery of high output voltages, potentially capable of charging a UAV. The proposed system was fabricated and measured, and its performance was assessed as a function of varying separation distances, folding configurations, and misalignment scenarios, demonstrating the validity of the concept.