Thermodynamic and structural properties of the tangent diatomic fluid are studied in the framework provided by the reference interaction site model (RISM) theory, coupled with a modified hypernetted chain closure. The enforcement of the internal thermodynamic consistency of the theory is described in detail. The results we obtain almost quantitatively agree with available or newly generated simulation data. We envisage the possibility to characterize real colloidal particles of dumbbell shape, and to extend the consistent RISM formalism to generic molecular fluids. (C) 2009 Elsevier B. V. All rights reserved.