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Terahertz vortex beams with different superposition of the orbital angular momentum l=±1, ±2, ±3, and ±4 and spin angular momentum σ=±1 were used to study antiferromagnetic (AFM) resonances in TbFe_{3}(BO_{3})_{4} and Ni_{3}TeO_{6} single crystals. In both materials we observed a strong vortex beam dichroism for the AFM resonances that are split in external magnetic field. The magnitude of the vortex dichroism is comparable to that for conventional circular dichroism due to σ. The selection rules at the AFM resonances are governed by the total angular momentum of the vortex beam: j=σ+l. In particular, for l=±2, ±3, and ±4 the sign of l is shown to dominate over that for conventional circular polarization σ.