The spectrum of the (A)over-tilde(2)Pi(g) <-- (X)over-tilde(2)Pi(u) 0(0)(0) band system of the triacetylene cation and isotopic derivatives DC6H+ and C6D2+ have been studied at Doppler-limited resolution using frequency modulation absorption spectroscopy. The ions were generated in a liquid-nitrogen-cooled hollow cathode discharge incorporated in a White cell. A discharge modulation in combination with the frequency modulation technique was used to enhance the detection sensitivity. Analyses of the rotational structure yield accurate rotational and spin-orbit interaction constants of triacetylene cation in the two electronic states and information on its geometry.