A combination of the mean-field theory and the random phase approximation is used to describe the effect of charge inversion ( overcharging) of a spherical penetrable microgel particle by oppositely charged multiarm star polyelectrolytes in dilute solution. The overcharging is shown to occur due to the gain in the electrostatic self-energy and in the elastic free energy of the star macromolecules, while counterions can either promote or suppress the effect. It is shown that many parameters, such as the densities of the microgel and the stars, the fraction of charged units, etc., control the overcharging.