A new theory based on the Ornstein-Zernike integral equation and applicable to any hard-body molecular fluid is proposed. The theory approximates the bridge function of the molecular fluid by the hard-sphere bridge function with an angular-dependent hard-sphere diameter. The theory is tested on the homonuclear hard-dumbell system over a wide range of elongations and densities. The predicted compressibility factors are numerically indistinguishable from available computer simulation results and the theory also gives a very good description of the pair distribution function, as represented both by the spherical harmonic expansion coefficients and by the site-site distribution functions.