  We propose a new mechanism for generating a single transverse spin asymmetry
(STSA) in polarized proton-proton and proton-nucleus collisions in the
high-energy scattering approximation. In this framework the STSA originates
from the q->q G splitting in the projectile (proton) light-cone wave function
followed by a perturbative (C-odd) odderon interaction, together with a C-even
interaction, between the projectile and the target. We show that some aspects
of the obtained expression for the STSA of the produced quarks are in
qualitative agreement with experiment: STSA decreases with decreasing
projectile x_F and is a non-monotonic function of the transverse momentum k_T.
In our framework the STSA peaks at k_T near the saturation scale Q_s. Our
mechanism predicts that the quark STSA in proton-nucleus collisions should be
much smaller than in proton-proton collisions. We also observe that in our
formalism the STSA for prompt photons is zero.
