Absorption and fluorescence spectroscopies with linearly polarized light are applied to study the anisotropic behavior of a fluorescence dye (rhodamine 6G, R6G) adsorbed in ordered clay (laponite, Lap) particles. Films elaborated by the spin-coating technique provide a parallel stacking of clay layers in the supported substrates. The posterior intercalation of the R6G molecules into the interlayer space of Lap films with a preferential orientation with respect to the normal to the clay layers gives rise to a macroscopic orientation of dye molecules into the 2D surfaces. Such an organization induces an anisotropic behavior with a photoresponse of dye/clay films to the plane of the polarized light. A mathematic procedure, based on the evolution of the fluorescence anisotropy with the twisting angle of the films with respect to the excitation light, is used to evaluate the preferential orientation of R6G molecules in Lap films. The fluorescence method can be extended to study the preferential orientation of fluorescent molecules adsorbed in any organized rigid 2D system.