The growth of 3C-SiC nano-crystal (NC) on 10 miscut Si(001) substrate by CO2 thermal treatment is investigated by scanning and high resolution transmission electron microscopies. The vicinal Si(001) surface was thermally oxidized prior to the annealing at 1100 C under CO2 atmosphere. The influence of the atomic steps at the vicinal SiO2/Si interface on the SiC NC growth is studied by comparison with the results obtained for fundamental Si(001) substrates in the same conditions. For Si miscut substrate, a substantial enhancement in the density of the SiC NCs and a tendency of preferential alignment of them along the atomic step edges is observed. The SiC/Si interface is abrupt, without any steps and epitaxial growth with full relaxation of 3C-SiC occurs by domain matching epitaxy. The CO2 pressure and annealing time effect on NC growth is analyzed. The as-prepared SiC NCs can be engineered further for potential application in optoelectronic devices and/or as a seed for homoepitaxial SiC or heteroepitaxial GaN film growth.