A theory, based on a modified Poisson-Boltzmann equation, is presented that allows us to calculate the excess interfacial tension of an electrolyte-oil interface accurately. The chaotropic (structure-breaking) ions are found to adsorb to the water-oil interface as the result of large polarizability, weak hydration, and hydrophobic and dispersion interactions. However, kosmotropic (structure-making) anions as well as potassium and sodium ions are found to be repelled from the interface. The adsorption of I(-) and ClO(4)(-) is found to be so strong as to lower the interfacial tension of the water-oil interface, in agreement with the experimental data. The agreement between the calculated interfacial tensions and the available experimental data is very good. The theory is used to predict the interfacial tensions of six other potassium salts, for which no experimental data is available at the moment.