First-principles calculations based on density functional theory (DFT) and the pseudopotential method have been used to study the adsorption of CO molecules on the in-plane Ti cation sites of the rutile (TiO2)(110) surface, in the absence of oxygen vacancy sites. The calculations employ slab geometry and periodic boundary conditions with full relaxation of all atomic positions. The accuracy of the theoretical method used in this study was verified by calculations on the bulk TiO2 crystal, bare surface and on the isolated CO molecule. As shown by the full relaxation of the atomic system, the CO molecule is vertically adsorbed on the TiO2(110) surface. There is a clear preference for the Ti-CO orientation compared to the Ti-OC configuration. In the first case the CO molecule is adsorbed at a distance of 2.320-2.376 Angstrom from the 5-fold-coordinated Ti site, while in the latter case the distance is larger, between 2.666 and 2.701 Angstrom. At half coverage the adsorption energies of 11.1 and 2.71 kcal/mol have been determined for Ti-CO and Ti-OC binding configurations, respectively, in good agreement with recent determinations based on temperature-programmed desorption experiments (9.9 kcal/mol). At full coverage the adsorption energies were found to decrease by 2-3 kcal/mol relative to the half coverage case due to the repulsion between the CO molecules. The lack of large chemical effects indicates that the adsorption takes place through a predominantly physisorption mechanism.