We study a weighted asymmetry in the azimuthal distribution of photon-jet pairs produced in the process pp→γ jet X with a transversely polarized proton. We focus on the contribution of the Sivers effect only, considering experimental configurations accessible at the Relativistic Heavy Ion Collider. We show that predictions for the asymmetry, obtained in terms of gluonic-pole cross sections calculable in perturbative QCD, can be tested and clearly discriminated from those based on a generalized parton model, involving standard partonic cross sections. Experimental measurements of the asymmetry will therefore test our present understanding of single-spin asymmetries. © 2007 The American Physical Society.