We calculated the site-site radial distribution functions for binary mixtures of tert-butyl alcohol (TBA) and water over the whole range of TBA molar fraction. The description uses the reference interaction site model (RISM) integral equation theory in the dielectrically consistent approach of Perkyns and Pettitt (DRISM), and the closure approximation of Kovalenko and Hirata (KH) providing appropriate description for association of polar molecular species of density ranging from gas to liquid. We employed the extended simple point charge (SPC/E) model for water, and the optimized potential for liquid simulations (OPLS) force field for TBA. The partial radial distribution functions obtained for the TBA-water mixture are in qualitative agreement with those available from neutron diffraction experiments and molecular dynamics simulations. It is found that hydrogen bonds between all species are enhanced with rise of the TBA concentration. The tetrahedral-like network of hydrogen bonding in dilute TBA aqueous solution gradually turns into the zigzag-like structure for a high TBA concentration. In dilute aqueous solution, TBA molecules cluster by the hydrophobic methyl groups, whereas their hydroxyl groups are incorporated into the water hydrogen-bonding cage surrounding the TBA aggregate. In concentrated TBA, water as well as TBA molecules associate into the zigzag-like hydrogen-bonding chains. The present work shows that the RISM/KH theory is able to qualitatively predict the association structure of alcohol-water liquid mixtures.