Titanium dioxide (TiO2) nanorods are widely employed in many energy-related applications thanks to their peculiar electronic and physicochemical properties. Here we report a periodic DFT and DFT-D study of the three most exposed surfaces of stoichiometric anatase TiO2 nanorods, i.e., (100), (001) and (101). On these surfaces, we investigated the adsorption of a tertiary amine (trimethylamine, TMA): Energetic, structural and electronic features have been characterized, paying particular attention on the effects of dispersion forces on the adsorption process. We found evidence of the formation of a coordinative bond between the molecules and the titanium site of adsorption. As expected, the inclusion of dispersion correction strongly enhances the adsorption process. Moreover, in some cases TMA adsorption introduces new electronic states at the edge of the valence band. Overall, our results provide new insights on the interactions between TiO2 nanorods and nitrogen compounds, which have many scientific and technological implications