The possibility of resonant conversion of wave fields oriented along the orthogonal sinusoidal conductors forming a woven mesh structure has been experimentally investigated using THz time-domain spectroscopy. This coupling, which enables the conversion of wave energy between surface waves appearing at co- and cross-oriented wires, results in a 90° rotation of the polarization of the waves transmitted through the woven mesh. A strong dependence of the phenomenon on the orientation of the woven mesh relative to the propagation direction and polarization of the incident THz waves has been shown and discussed. We believe that such properties of the metallic woven meshes can open up new prospects for investigating the interaction of THz waves with structured-wire grids.