Strong resonant light scattering by individual spherical Si nanoparticles is experimentally demonstrated, revealing pronounced resonances associated with the excitation of magnetic and electric modes in these nanoparticles. It is shown that the low-frequency resonance corresponds to the magnetic dipole excitation. Due to high permittivity, the magnetic dipole resonance is observed in the visible spectral range for Si nanoparticles with diameters of {\~}200 nm, thereby opening a way to the realization of isotropic optical metamaterials with strong magnetic responses in the visible region.