Peaks due to the rainbow scattering in elastic collisions of Ar+ ions with ground state CH4 molecules were observed in the differential cross section at laboratory energies from 20 to 80 eV superimposed on an oscillatory structure which is attributed to the accidental resonant electron transfer between collision partners. The rainbow peaks are clearly seen when the differential cross section is plotted in a reduced form. Indeed, each rainbow peak appears at the reduced scattering angle of about 290 eV-degrees. Classical calculations are fitted to the experimental cross sections with the use of the 12-6-4 potential. This potential contains an adjustable force parameter γ ranging from 1 to 0 according to how the charge-induced dipole interaction has a dominant role in the collision. The best fit is obtained when the potential depth is 2.7 eV and the interatomic distance at the potential well minimum is 2.4 Å for γ = 0.4.