A single mode cw dye laser excitation along with velocity modulation detection was used to record between 17 100 and 18 600 cm(-1) the absorption spectrum of the (3) Delta(3d4s)-X-3 Phi(3d(2)) visible system of TiCl+ produced in an ac glow discharge with a gas mixture of He/TiCl4. The rotational structure of the (0,0) and (1,0) vibrational bands has been observed and fully analyzed for the main isotopomer (TiCl+)-Cl-35 as well as for (TiCl+)-Cl-37. Beside the confirmation of the nature of the two electronic states, the observation of the forbidden (3) Delta(2)-(3) Phi(2) and (3) Delta(3)-(3) Phi(3) intercombination transitions allowed the first experimental determination of the spin-orbit constants and a detailed characterization of both the (3) Delta and (3) Phi states through a matricial fitting of the data. Molecular parameters have been derived.