A regenerated cellulose fiber is, in contrast to cotton, a man-made fiber. In the fiber production, the cellulose polymer is subject to various processing steps, affecting the underlying molecular orientation distribution, which is a determining factor for mechanical properties of the fiber. In this work, the molecular orientation distribution was determined in a C-13 natural abundance Lyocell regenerated cellulose fiber bundle using rotor synchronized magic angle spinning NMR spectroscopy (ROSMAS) to investigate the chemical shift anisotropy (CSA). The recorded signal intensities were compared with an analytical model of the experiment to find the order parameters reflecting the orientation of the fiber. The CSA tensor was calculated using density functional theory for the crystalline cellulose II structure, commonly found in regenerated cellulose, and is required as an input parameter. The expected order parameter values were only found when approximating the glycosidic bond and its CSA tensor as being parallel to the molecular frame with the order parameter P2=0.45 +/- 0.02 compared to P2=0.46 +/- 0.02 obtained with wide angle X-ray scattering on a fiber bundle. To make this method accessible to the community, we distribute the Matlab script for the simulation of spectra obtained by the ROSMAS experiment at github.com/LeoSvenningsson/ROSMAS.