  We study chirality of the vorticity of the Universe within the
Einstein-Cartan cosmology. The role of the spin of fermion species during the
evolution of the Universe is studied by averaged spin densities and
Einstein-Cartan equations. It is shown that spin density of the light Majorana
neutrinos acts as a seed for vorticity at early stages of the evolution of the
Universe. Its chirality can be evaluated in the vicinity of the spacelike
infinity. It turns out that vorticity of the Universe has right-handed
chirality.
