We review the baryon asymmetry generated in the early Universe in the framework of the metric-spinor gravity with the Holst term, which accounts for the Barbero-Immirzi parameter. For the generation of the matter-antimatter asymmetry, we have considered the model in which the time derivative of the Ricci scalar couples with matter currents (this model is known in the literature as gravitational baryogenesis). By using the current bounds on the parameter of the asymmetry, the ratio of baryon number to the entropy density, we infer a bound on the parameters characterizing the model under consideration (that is, the cosmological model in the presence of the torsion and Barbero-Immirzi parameter).