A characteristic length scale of the structure of a thixotropic colloidal clay suspension of discotic texture was demonstrated by static light scattering. The length scale, of the order of a micron, corresponds to a fractal dimension that increases from 1 to 1.8 close to a critical volume fraction. Simultaneously, the change in yield stress with the volume fraction was studied by the vane method. A scaling law enabled these fractal dimensions to be correlated with the effect of the volume fraction on the yield stress.