The self-consistent approach and the rotating group representation theory have been used to calculate the effective conductive sensor of the polycrystalline textured medium, consisting of anisotropic spherical crystallites oriented in space according to a certain probability law, that implies the uniaxial texture existence. The analytical solution for two cases - if the crystallites are slightly anisotropic and if the angle between one of the crystallites axes and the texture axis is small - has been obtained.