  We present estimates of transverse single-spin asymmetry in prompt photon
production in the scattering of low virtuality photons off a polarized proton
target and discuss the possibility of using this as a probe to get information
about the gluon Sivers function (GSF). Using a generalized parton model (GPM)
framework, we estimate the asymmetries at electron-ion collider energy
($\sqrt{s}$ =140 GeV) taking into account both direct and resolved photon
processes and find that the dominant contribution, up to $10\%$, comes from
quark Sivers function (QSF) while the contribution from GSF is found to be up
to $2\%$. However, upon taking into account the effects of the
process-dependent initial and final state interactions through the color-gauge
invariant generalized parton model approach we find that the situation is
significantly changed, with near zero contributions from the QSFs and up to a
$1\%$ level contribution from the \textit{f}-type GSF. Our results indicate
that this process may be useful for distinguishing between GPM and color-gauge
invariant generalized parton models and can be used as a good probe of
\textit{f}-type GSF.
