A method of measuring the thickness of a fiber texture wound on an impregnation mandrel for fabricating an annular structural part of a turbine engine out of composite material, the method including, prior to winding the fiber texture, acquiring a reference distance between an outside surface of the impregnation mandrel and a distance sensor positioned facing the outside surface of the impregnation mandrel, while winding the fiber texture, acquiring at least one real distance between the distance sensor and the outside surface of the fiber texture wound on the impregnation mandrel, and calculating the real thickness of the fiber texture wound on the impregnation mandrel by subtracting the real distance from the reference distance.