An apparatus and method for mounting a valve stem to the rim of an vehicle wheel includes engaging a valve stem with a robotic manipulator, moving the valve stem relative to the rim along a programmable path of travel, coaxially aligning the valve stem with the aperture in the rim, and inserting the valve stem through the aperture in the rim. Preferably, the aperture location in the rim is determined at a gauging station by a machine vision system. If necessary, a power-actuated nut runner is used to tighten a nut over the valve stem. Alternately, the gauging station can use a table which rotates the wheel about a central axis, and an optical sensor detects the location of the aperture. Optionally, a probe mounted on the gauging station can be extended into the aperture to confirm the aperture position and to reposition the rim slightly if required.