  We present the first steps in an effort to incorporate the physics of
transverse spin asymmetries into the saturation formalism of high energy QCD.
We consider a simple model in which a transversely polarized quark scatters on
a proton or nuclear target. Using the light-cone perturbation theory the hadron
production cross section can be written as a convolution of the light-cone wave
function squared and the interaction with the target. To generate the single
transverse spin asymmetry (STSA) either the wave function squared or the
interaction with the target has to be T-odd. In this work we use the
lowest-order q->qG wave function squared, which is T-even, generating the STSA
from the T-odd interaction with the target mediated by an odderon exchange. We
study the properties of the obtained STSA, some of which are in qualitative
agreement with experiment: STSA increases with increasing projectile x_F and is
a non-monotonic function of the transverse momentum k_T. Our mechanism predicts
that the quark STSA in polarized proton--nucleus collisions should be much
smaller than in polarized proton--proton collisions. We also observe that the
STSA for prompt photons due to our mechanism is zero within the accuracy of the
approximation.
