High-resolution measurements of the X-ray absorption coefficient were made around and up to 1000 eV above the titanium K-edge of TiC1-x samples (0.5 ≤ 1-x ≤ 0.97). When increasing the carbon vacancy content x, (i) the positive effective charge of titanium deduced from the edge-shift decreases, (ii) the bottom of the titanium 4p bands (situated at 10-15 eV above the Fermi level EF in TiC0.97) moves down progressively towards EF. From the increased damping of the Exafs oscillations with non-stoichiometry, average mean-square static relative displacements of titanium-titanium and titanium-carbon first neighbours are evaluated. A simple model where each carbon vacancy repells its first neighbours Ti by 0.08 Å is proposed.