The site-site Ornstein-Zernike equation with the RISM closure is used to study the binding of calcium ions to the protein calbindin. A static, charged hard-sphere model is used for the protein, and the primitive model is used for the surrounding electrolyte solution. The free energy of calcium binding to the protein over a range of ambient electrolyte concentrations and mutations was determined from the random phase approximation. Theory is found to be in remarkably good agreement with computer simulation predictions. Extensions of the theory to include a molecular description of the solvent are discussed.