A theory for a new laser guide star technique is developed. This technique, for the first time, permits the sensing of a full-aperture tilt of the atmospheric wave front distortions using a laser guide star, eliminating one of the fundamental limitations of adaptive optics. By using a detailed analysis of the laser guide star image jitter for a conventional scheme and for its possible modifications, it is shown that, because of reciprocity of propagation paths, a conventional laser beacon is unable to sense a full aperture tilt and can be only used to measure the higher-order wavefront distortions. The full aperture tilt can be measured with a divergent beam if its effective size at a laser beacon altitude coincides with the radius of a receiving telescope. Estimates of the modified laser guide star image jitter rms, signal-to-noise ratio, and the mean square deviation between the instantaneous tilts for the modified laser beacon and a natural star are obtained, and it is shown that the proposed technique is practical.