This paper presents an efficient coil design for a mm-sized micro-robot which generates a propulsion force and torque and receives electrical energy using a wireless power transfer system. To determine the most efficient coil structures and produce propulsion and torque on the micro-robot, both helical and spiral coil modeling was conducted, and analytical formulations of the propulsion force and torque were derived for helical and spiral coil structures. Additionally, the dominant dimensional factors for determining propulsion and coil torque were analyzed in detail. Based on the results, an optimum coil structure for generating maximum force on the micro-robot was developed and is herein presented with dimensional analysis. Simulations and experiments were also conducted to verify the design, and good agreement was achieved. A 3-mm micro-robot that simultaneously generated a propulsion force and torque and received electrical energy via wireless power transfer was successfully fabricated using the proposed method and verified.