We study the production of transversely polarized A hyperons in high-energy collisions of protons with large nuclei. The large gluon density of the target at saturation provides an intrinsic semi-hard scale which should naturally allow for a weak-coupling QCD description of the process in terms of a convolution of the quark distribution of the proton with the elementary quark-nucleus scattering cross section (resummed to all twists) and a fragmentation function. In this case of transversely polarized A production we employ a so-called polarizing fragmentation function, which is an odd function of the transverse momentum of the A relative to the fragmenting quark. Due to this k(i)-odd nature, the resulting A polarization is essentially proportional to the derivative of the quark-nucleus cross section with respect to transverse momentum, which peaks near the saturation momentum scale. Such processes might therefore provide generic signatures for high parton density effects and for the approach to the "black-body" (unitarity) limit of hadronic scattering. (C) 2003 Elsevier Science B.V. All rights reserved.