The correlations between process conditions, microstructure, and mechanical properties of additively manufactured components are not fully understood yet. In this contribution, three different hatch strategies are used to fabricate rod-like samples from S316L stainless steel, which are further investigated using synchrotron diffraction, optical microscopy, and tensile tests. The results indicate the presence of ⟨110⟩ biaxial and fiber textures, whose sharpness depends on the applied hatch strategy. Mechanical tests reveal a strong correlation of the samples’ response to the observed anisotropy in the plane perpendicular to the build direction. Even though the average yield and ultimate tensile strengths of around 475 and 500 MPa, respectively, do not differ significantly, the stress–strain behavior can be correlated with the observed in-plane anisotropy. Particularly, twinning-induced plasticity, a distinct increase of the work hardening rate at larger strains and elliptical necking are observed in some samples with biaxial (Goss) texture. These findings indicate that texture design by means of applying dedicated hatch strategies can be used to effectively tune the multiaxial deformation behavior of components produced by laser powder bed fusion.