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Thin film shape memory alloys are a promising material for use in microscale devices for actuation and sensing due to their strong actuating force, substantial displacements, and large surface to volume ratios. NiTi, in particular, has been of great interest due to its biocompatibility and corrosion resistance. Effort has been directed toward adjusting the microstructure of as-deposited films in order to modify their shape memory properties for specific applications. The anisotropy of the shape memory and superelastic effects suggests that inducing preferred orientations could allow for optimization of shape memory properties. Limited work, however, has been performed on adjusting the crystallographic texture of these films. In this study, thin film NiTi samples are processed using excimer laser crystallization and the effect on the overall preferred orientation is analyzed through the use of electron backscatter diffraction and X-ray diffraction. A three-dimensional Monte Carlo grain growth model is developed to characterize textures formed though surface energy induced abnormal grain growth during solidification. Furthermore, a scaling factor between Monte Carlo steps and real time is determined to aid in the prediction of texture changes during laser crystallization in the partial melting regime.