An angle-measuring device includes a first group of components and a second group of components that are rotatable relative to each other about an axis. The first group includes a carrier element for enclosing a shaft and on which a graduation disk is secured, a connecting element, and a device for affixing the connecting element relative to the carrier element. The second group includes a sensor element for scanning the graduation disk. The carrier element and the connecting element are arranged such that the connecting element is able to be brought into operative connection with the carrier element so that torque is transmittable with positive locking between the connecting element and the carrier element about the axis. The connecting element is able to be brought into a positive-locking position by axial displacement by the device for affixing the connecting element, and is able to be prestressed radially against the shaft.