Shape Memory Alloys (SMAs) are a class of metallic multi-functional materials which possess sensing and actuation capabilities, thanks to their unique ability to couple thermal and mechanical fields. NiTi-based Shape Memory Alloys exhibit properties which guarantee their high performance in adverse environments and, with the added benefit of two functionalities, the Shape Memory Effect and Superelasticity, these materials have become ideal candidates for a variety of applications. Spatial orientation of the NiTi crystals is crucial for achieving the superelastic functional response. According to studies on NiTi single crystals, when the grains adopt a [001] orientation along the direction of compression, slip is inhibited in the austenite phase and recoverable transformation strains similar to the theoretically estimated values of 5.3% are possible, defining the benchmark for superelastic responses. Additive Manufacturing techniques, due to their inherent thermal processing conditions, have created unprecedented opportunities for fabrication of NiTi-based Shape Memory Alloys so that the thermomechanical behaviour of the material can be tailored to any application is intended for. During Laser- Powder Bed Fusion, the scanning strategy influences the thermal processing to which the alloy is subjected, affecting its solidification process as well as the heat fluxes and temperature gradients that arise during manufacturing. Meanwhile, it can play a decisive role in achieving epitaxial solidification of columnar grains extending over multiple deposition layers. In this study, five different scanning strategies were employed during Laser-Powder Bed Fusion (L-PBF) of a Ni-rich NiTi alloy and were evaluated with respect to the grain morphology and crystallographic texture that developed, as well as the superelastic response of the samples produced. It was found that a 67° interlayer rotation of the scanning vector promotes the fusion of neighbouring melt pools, resulting in columnar grains that solidify epitaxially along the build direction (BD) of the sample. Meanwhile, a strong ⟨001⟩ fibre texture emerges along the BD. The superelastic response was stabilised at 4.5% recoverable strain with 74.2% recovery ratio after 16 cycles of axial compression loading. When an island scanning pattern was incorporated into the 67° rotation scanning strategy, the crystallographic texture strengthened and the superelastic response improved, (5.0% stabilised recoverable strain and 84% recovery ratio). Furthermore, an increase in the volumetric energy density, achieved by using a flat top laser beam, produced a nearly single-crystalline microstructure, with the highest intensity of the ⟨001⟩∥BD texture. The superelasticity in this case was stabilised at 5.5% recoverable strain with 91.5% recovery ratio. The effect of the loading direction on the superelastic response was also investigated, as was the nature of the residual strain left in the samples after their superelasticity stabilised. Therefore, this study successfully demonstrated that the scanning strategy can be a vital tool in designing the crystallographic texture and the grain morphology of NiTi parts fabricated by L-PBF, and this way, effectively tailor the superelastic functional behaviour to specific requirements of potential applications.