It is well known that galaxies rotate and their angular momenta are correlated over relatively large scales. However, in a perfect fluid vorticity in conserved and cannot be generated. The particle nature of dark matter, leading to velocity dispersion and shell crossing, is at the origin of cosmological vorticity generation. These are non-perturbative processes which must be studied numerically. In this paper we investigate the generation of vorticity during the formation of cosmological large scale structure using the public relativistic N-body code gevolution. We test several methods to compute the vorticity power spectrum and we study its convergence with respect to the mass and grid resolution of our simulations. We determine the power spectrum, the spectral index on large-scales, the amplitude of the peak position and their time evolution. We also compare the fluid vorticity with the vector perturbations of the metric. Our results are accompanied by resolution studies and compared with previous studies in the literature.