A new micro-rotating platform based on flexure hinges was designed by using piezoelectric actuation method to meet the precision requirement of micro/nano precision positioning. The input displacement of the mechanism was magnified by the first order magnifying mechanism with the right angle flexible hinge, and the magnification and rotation angle were analyzed theoretically. The theoretical value of the output displacement of the micro rotating positioning platform was compared with the ANSYS simulation value, and the theoretical value was basically consistent with the simulation one. The stress and deformation of the flexure hinge of the micro rotating positioning platform were verified, and the mechanical properties of the selected material met the design requirements when the output displacement was satisfied.