The result of adding the spin density term in heavy-ion interaction potentials is studied for the first time, especially for unclosed shell nuclei. For the energy density functional of Skyrme interaction, the spin density contribution is derived for nuclei with an even number of valence particles (or holes). The calculations are made for light nuclei, using both the shell-model and Fermi-type nucleon densities. The interaction potential is calculated in the proximity theorem, using corrected Thomas-Fermi approximation for the kinetic energy density. Only the repulsive spin density contribution is found to be significant, which cancels a part of attraction in the total interaction potential.