Ultrathin MoS2 has shown remarkable characteristics at the atomic scale with immutable disorder to weak external stimuli. Ion beam irradiation unlocks the potential to selectively tune the size, concentration, and morphology of defects produced at the site of impact. Combining experiment, atomistic simulation and deep learning, we show that irradiation-induced defects can induce a rotation-dependent moiré pattern in vertically-stacked homobilayers of MoS2 by deforming the atomically thin material and exciting surface acoustic waves (SAWs). Additionally, by probing the intrinsic defects and atomic environment, we see a direct correlation to the stress contribution that lattice disorder and various polymorphs have. The method introduced in this paper sheds light on how engineering defects in the lattice gives full control on the angular mismatch in van der Waals (vdW) solids.