The interaction energy is studied for the coupling of axial torsion fields with photons in the presence of an external electromagnetic field. To this end, we compute the static quantum potential. Our discussion is carried out using the gauge-invariant but path-dependent variables formalism, which is alternative to the Wilson loop approach. Our results show that the static potential is a Yukawa correction to the usual static Coulomb potential. Interestingly, when this calculation is done by considering a mass term for the gauge field, the Coulombic piece disappears leading to a screening phase. © 2010 Springer Science+Business Media, LLC.