A device for changing the rotational angle position of a pneumatic tire relative to a rim, on which the pneumatic tire is fitted to the rim, includes a manipulating device with a gripper adapted to be rotated by a positionable rotary drive mechanism and having radially adjustable gripper fingers with oppositely facing lift-off devices. Via the gripper it is possible to load a wheel into a clamping fixture, and following unseating of the tire beads from the clamped rim the pneumatic tire can be rotated relative to the rim through a computed angular difference.