We have measured the angular distributions for ¹²C ion beam elastically scattered from ¹²C target of thickness 17.4 μg/cm² at energies 15, 18 and 21 MeV which is close to the Coulomb barrier energy for ¹²C + ¹²C nuclear system. The elastic scattering of ¹²C beam on ¹²C was analysed also at different energies (139.5, 158.8, 180, 240, 288.6, 300, 360 and 420 MeV) from literature in order to obtain the global optical potential parameters, which could fairly reproduce the experimental data. The experimental results were analysed within the framework of both the optical model and the double folding potential obtained with different density-dependent NN interactions which give the corresponding values of the nuclear incompressibility K in the Hartree-Fock calculation of nuclear matter. The agreement between the experimental results and the theoretical predictions in the whole angular range is fairly good.