We present estimates of transverse single-spin asymmetry (TSSA) 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 (EIC) energy ( √ s =140 GeV) taking into account both direct and resolved photon processes and find that the dominant contribution, upto 10%, comes from quark Sivers function (QSF) while the contribution from GSF is found to be upto 2%. However, upon taking account the effects of the processdependent initial and final state interactions through the color gauge invariant generalized parton model (CGI-GPM) approach we find that the situation is significantly changed, with near zero contributions from the QSFs and upto a 1% level contribution from the f-type GSF. Our results indicate that this process may be useful for distinguishing between GPM and CGI-GPM models and can be used as a good probe of f-type GSF.