  We compute the transverse single spin asymmetry in forward $p^\uparrow p \to
hX$ and $p^\uparrow A \to hX$ collisions from the odderon mechanism originally
suggested by Kovchegov and Sievert [1]. Working in the hybrid approach of the
Color Glass Condensate effective theory we firstly identify the relevant
collinear parton distribution function (PDF) of the transversely polarized
proton $p^\uparrow$ as the intrinsic twist-3 $g_T(x)$ distribution. We further
argue that the complete polarized cross section also contains contributions
from the kinematical and the dynamical twist-3 PDFs, in addition to the
intrinsic twist-3 PDF. By restricting to the Wandzura-Wilczek approximation,
where the dynamical twist-3 PDFs are dropped, we find that the odderon
contribution to the polarized cross section for inclusive hadron production is
exactly zero at the next-to-leading order in the strong coupling.
