Relativistic complete-active space self-consistent field and multireference configuration interaction computations including spin-orbit coupling are made an the TaC2+ cation, the most abundant of metal carbides observed in direct laser vaporization and Knudsen effusion-mass spectrometric experiments. The suggested mechanism of TaC2+ formation via recombination reactions between Ta+ and C-2 is consistent with the calculated potential energy curves for the low-lying electronic states. Two nearly degenerate unsymmetrical Linear (Ta-C-C+) and symmetrical C-2 upsilon(C-Ta-C+) isomers suggest that the products can include a mixture of both isomers.