We report the first observation of the lock-in transition in artificial superconducting superlattices, which takes place in tilted magnetic fields. The measurements were carried out on the Mo/Si layered system. The temperature dependence of the critical angle for the trapping of the vortices in the orientation parallel to the layer planes is determined by the previously known resistive method and by a new method based on the effect of commensurability between the intervortex distance and the superlattice wavelength. The temperature dependences of the critical angle obtained by the two methods practically coincide. The experimental results are consistent with the theoretical predictions of Feinberg and Villard.