A remote center of motion robotic arm includes an arm unit, a drive unit and a control unit. The arm unit includes a base seat, a first link rotatable relative to the base seat, a mount seat, and a second link pivoted to the first link and rotatable relative to the mount seat. The drive unit includes first and second drive motors for rotating the first and second links. The control unit controls the drive unit to move the first and second links from an initial position to an objective position, such that the relative position between the base seat and the mount seat is maintained after the movement of the first and second links.