Device and method for the finishing machining of an internal face of a workpiece, such as the track of a ball screw, including a workpiece holder and a finishing tool held on a finishing tool holder. A rotary drive is provided, by which the workpiece holder and the finishing tool is rotationally driven relative to one another about a rotational axis. A linear drive is provided, by which the finishing tool held on the finishing tool holder and the workpiece holder is driven in a translatory manner relative to one another along the rotational axis. An oscillating drive is provided, by which the finishing tool held on the finishing tool holder and the workpiece holder is driven in an oscillating manner relative to one another in the direction parallel to the rotational axis and wherein the finishing tool is pivotably held on the finishing tool holder about a pivot axis.