The use of hard X-rays (60-300 keV) for diffraction studies of disordered materials has several advantages: higher resolution in direct space, smaller correction terms, removal of truncation effects, the possibility for operating in extreme environments and for direct comparison between X-ray and neutron data. A feasibility study of amorphous silica has been performed at 95 keV, using a wiggler synchrotron beam-line at HASYLAB and a cylindrical sample, 3 mm in diameter. The range of Q between 0.8 and 32 Angstrom(-1) was covered. A thorough discussion of the experimental challenges is given. The resulting systematic error intrinsic to the scattering process (not including errors in the form-factors) is found to be of the order of 0.2%. The data have been analyzed in terms of a model of the short-range order. The O-Si-O bond angle distribution is found to be nearly Gaussian, centered around 109.3(3)degrees with a rms value of 4.2(3)degrees. For the Si-O-Si bond angle, several types of distribution V(alpha) = V-1(alpha) sin(alpha) were investigated. Best fits were obtained for rather broad distributions with V having its maximum at 147 degrees and V-1 at 180 degrees.