The coordination of cis(CO)–trans(I)-Ru(4,4′-dicarboxylate-2,2′-bipyridine)(CO)2I2 on an anatase (101) surface was investigated using a computational density functional method. The adsorbate is able to interact with the anatase surface by one or two carboxylate substituents of the bipyridine ligand. Three of the studied coordination modes involved a single carboxylate as the binding group, including monodentate (1M), bidentate chelating (1BC) and bidentate bridging (1BB) modes. The possibility of monodentate binding via both carboxylate groups in (2M) was also studied. The results showed that the multidentate binding is clearly preferred over monodentate coordination. The stability of the modes increased in the order 1M, 1BC, 1BB and 2M. The flexibility of the bipyridine ligand was found to be the key factor in the binding via two carboxylate groups.