We propose a new method for dating ancient linen threads by inspecting their structural degradation by means of wide-angle X-ray scattering. X-ray dating of a textile sample can be performed nondestructively and on a submillimeter area, e.g., 0.2 0.5 mm2, exploiting new table-top X-ray micro-sources. A theoretical formula is derived for dating linen samples directly from wide-angle X-ray scattering measurements. Our preliminary results show that X-ray dating results are in agreement with other dating sources, such as the radiocarbon method and historical records, if some conditions are satisfied. Indeed, this new dating method can be applied only to threads not older than about thirty centuries because of the saturation of the structural degradation with age. Moreover, the method can be applied only on textiles in which cellulose degradation is mainly due by natural aging arising from thermal, hydrolytic, photolytic, photochemical, and oxidative processes. Analyses can be repeated several times on the same sample, which remains unaltered for other complementary characterization procedures. The proposed X-ray dating of some ancient linen fabrics opens the way to explore limits and potentialities of this new approach and to further develop a new dating method, alternative to the existing ones for specific applications in archeological studies.