We present an innovative microfabrication process to fabricate magnesium-based bioresorbable microelectromechanical systems (MEMS) by ion beam etching. This process enables the fabrication of thin biodegradable water-soluble passive electronic components with minimal exposure to aqueous media, by a novel physical vapor deposition, photolithography and dry etching sequence. We demonstrate the design, fabrication and characterization of frequency-selective magnesium RF micro-resonators in air and in water, and compare the results to values obtained by finite element modeling (FEM). Such resonators are candidates for selectively-addressable RF power receivers for bioresorbable wireless implantable medical devices.