A common optical potential for 4 He+ 12 C at intermediate bombarding energies, which is essential in analyzing exotic nuclei with 4 He clusters, was obtained based on the São Paulo potential (SPP). Among systematic optical potentials for 4 He+ 12 C, this potential has the merit of using a fixed imaginary part of Woods-Saxon form. By optical-model calculations, this potential reproduced the experimental elastic scattering angular distributions of 4 He+ 12 C well within the energy range of 26 A-60 A MeV. It was also applied successfully in calculations of the breakup reactions of 6 Li+ 12 C and 6 He+ 12 C with a three-body continuum discretized coupled-channels method.