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 () 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 -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 -type GSF.