Using the CO oxidation as a chemical probe, we perform a comprehensive ab initio study of catalytic activities of subnanometer gold clusters. Particular attention is placed on 12 different clusters in the size range of Au(16)-Au(35), whose atomic structures in the anionic state have been resolved from previous experiments. Adsorption energies of a single CO or O(2) molecule as well as coadsorption energies of both CO and O(2) molecules on various distinctive surface sites of each anionic cluster and their neutral counterpart are computed. In general, the anionic clusters can adsorb CO and O(2) more strongly than their neutral counterparts. The coadsorption energies of both CO and O(2) molecules decrease as the size of gold clusters increases with the exception of Au(34) (an electronic "magic-number" cluster). Besides the known factor of low coordination site, we find that a relatively small cone angle (<110°) associated with each surface site is another key geometric factor that can enhance the binding strength of CO and O(2). For the subnanometer clusters, although the size effect can be important to the strength of CO adsorption, it is less important to the activation energy. Using Au(34) as a prototype model, we show that strong CO and O(2) adsorption sites tend to yield a lower reaction barrier for the CO oxidation, but they have little effect on the stability of the reaction intermediate. Our calculations support the notion that CO and O(2) adsorption energies on the gold clusters can be an effective indicator to assess catalytic activities of subnanometer gold clusters. This systematic study of the site- and size-dependent adsorption energies and reaction pathways enables a quantitative assessment of the site-size-activity relationship for the CO oxidation on subnanometer gold clusters.