This study proposes that both constitutively and rhetorically (through ironic, inferential, and indirect application), Ps 106(105) serves as the substructure for Paul's argumentation in Rom 1:18-2:11. Constitutively, Rom 1:18-32 hinges on the triadic interplay between "they (ex)changed" and "God gave them over," an interplay that creates a sin-retribution sequence with an a-ba-ba-b pattern. Both elements of this pattern derive from Ps 106(105):20, 41a respectively. Rhetorically, Paul ironically applies the psalmic language of idolatrous "(ex)change" and God's subsequent "giving-over" to Gentiles. Aiding this ironic application is that Paul has cast his argument in the mold of Hellenistic Jewish polemic against Gentile idolatry and immorality, similar to Wis 13-15. In Rom 2:1-4, however, Paul inferentially incorporates a hypocritical Jewish interlocutor into the preceding sequence through the charge of doing the "same," a charge that recalls Israel's sins recounted in Ps 106(105). This incorporation then gives way to an indirect application of Ps 106(105):23, by means of an allusion to Deut 9-10 in Rom 2:5-11. Secondarily, this study suggests that Paul's argumentation exploits an intra-Jewish debate in which evocations of the golden calf figured prominently.