In this paper, we investigate the potential of reconfigurable intelligent surfaces (RISs) in facilitating passive/device-free three-dimensional (3D) drone localization within existing cellular infrastructure operating at millimeter-wave (mmWave) frequencies and employing multiple antennas at the transceivers. The developed localization system operates in the bi-static mode without requiring direct communication between the drone and the base station. We analyze the theoretical performance limits via Fisher information analysis and Cram\'er Rao lower bounds (CRLBs). Furthermore, we develop a low-complexity yet effective drone localization algorithm based on coordinate gradient descent and examine the impact of factors such as radar cross section (RCS) of the drone and training overhead on system performance. It is demonstrated that integrating RIS yields significant benefits over its RIS-free counterpart, as evidenced by both theoretical analyses and numerical simulations.