The developed microstructures and textures and their effect on the tensile behavior of a 316L austenitic stainless steel produced by powder bed fusion (PBF) were studied. The material printed with one set of printing parameters was tensile tested in three different directions. The microstructural analysis was conducted using electron microscopy. Referring to the build direction (BD) and the side direction (SD), which are parallel/crosswise to the laser scanning direction, the texture can be characterized by two strong components of <011>//BD and <001>//SD. The obtained steel samples exhibit the yield strength of 550 MPa–590 MPa depending on the tensile direction. The strengthening contributors to the PBF material were considered separately. Considering the microstructural grain size between the high angle boundaries and taking the dislocations of cellular structure as a part of dislocation density, the dislocation density is considered being the main strength contributor while the Taylor factor variety from about 2.9 to 3.2 for different directions revealed the strength anisotropy as an attribute of the texture.