The present paper uses mathematical analysis to investigate Rayleigh wave transference in an orthotropic layer. The considered model comprises an orthotropic layer covering a homogeneous isotropic micropolar half-space. The surface of the layer and the interface of the two media are taken to be corrugated. The dispersion relation is obtained in the determinant form, which describes the reliance of Rayleigh wave velocity on wave number. Some particular cases have also been deduced and are found to match existing results. The primary outcome of the present study is that the corrugation present in the structure has an influential impact on the velocity of the propagating wave. This impact has been presented through graphs. Moreover, the dynamic response of the layer’s height, elastic constant, material density of the orthotropic material, and micropolarity associated with the half-space on the phase velocity of Rayleigh waves have also been shown with the aid of graphs. The present paper finds its applications in the theoretical study of surface wave transference in anisotropic elastic structures.