The collisionless nature of dark matter, inducing velocity dispersion and shell crossing, is at the origin of cosmological vorticity generation. 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 vorticity extracted from our simulations with the vector perturbations of the metric. Our results are accompanied by resolution studies and compared with previous studies in the literature.