In this communication, a four-component Dirac theory of ionization of a hydrogen molecular ion, H⁺₂, in a super-intense laser field is presented. Analytic expressions for the spin-specific as well as the total ionization currents emitted from the ground state of the ion are derived. The results are given for arbitrary intensity, frequency, wavenumber and polarization of the field, and for the up or down spin of the bound and ionized states of the electron. They also apply for the case of inner-shell ionization of analogous heavier diatomic molecular ions. The presence of molecular two-slit interference effect, first found in the non-relativistic case, the spin-flip ionization current, and an asymmetry of the up- and down-spin currents similar to that predicted in the atomic case, is found to hold for the present relativistic molecular ionic case as well. The possibility of controlling the spin of the dominant ionization current in any direction by simply selecting the handedness of a circularly polarized incident laser field is pointed out. Finally, we note that the present results obtained within the strong field 'KFR' ansatz open up the way for an analogous fully relativistic four-component treatment for ionization of polyatomic molecules and clusters in super-intense laser fields.