The observed two-point angular correlation function, w(theta), of mJy radio sources exhibits the puzzling feature of a power-law behaviour up to very large (almost 10 degrees) angular scales which cannot be accounted for in the standard hierarchical clustering scenario for any realistic redshift distribution of such sources. After having discarded the possibility that the signal can be explained by a high density local source population, we find no alternatives to assuming that - at variance with all the other extragalactic populations studied so far, and in particular with optically selected quasars - radio sources responsible for the large-scale clustering signal were increasingly less clustered with increasing look-back time, up to at least z=1. The data are accurately accounted for in terms of a bias function which decreases with increasing redshift, mirroring the evolution with cosmic time of the characteristic halo mass, M_{star}, entering the non linear regime. In the framework of the `concordance cosmology', the effective halo mass controlling the bias parameter is found to decrease from about 10^{15} M_{sun}/h at z=0 to the value appropriate for optically selected quasars, 10^{13} M_{sun}/h, at z=1.5. This suggests that, in the redshift range probed by the data, the clustering evolution of radio sources is ruled by the growth of large-scale structure, and that they are associated with the densest environments virializing at any cosmic epoch. The data provide only loose constraints on radio source clustering at z>1 so we cannot rule out the possibility that at these redshifts the clustering evolution of radio sources enters a different regime, perhaps similar to that found for optically selected quasars. The dependence of w(theta) on cosmological parameters is also discussed. ; Comment: 9 pages, 8 figures. Accepted for publication on MNRAS