The structure of a colloidal dispersion consisting of anisometric natural clay particles (beidellite) was followed under shear-flow conditions by small-angle X-ray scattering (SAXS) measurements in a Couette-type cell. It is shown that in this shear-thinning dispersion an orientational order develops with increasing shear rate. By use of two different geometrical configurations for SAXS measurements, corresponding to incident beam parallel and perpendicular to flow velocity gradient (radial and tangential configurations, respectively), it is observed that SAXS patterns are anisotropic in both geometries, meaning that particles tend to align along a preferred orientation with their normal in velocity gradient direction, and further they partly rotate around flow streamlines. Quantitative interpretation of these results is successfully achieved upon derivation of a probability distribution function accounting for biaxial particle orientation. From this distribution and following geometrical arguments, the viscosity of the suspension was calculated for each shear rate and found to correctly compare with rheological measurements, thereby appropriately relating the anisotropy of the SAXS patterns to macroscopic flow behavior of the suspension.