To circumvent CRISPR-Cas immunity, phages express anti-CRISPR factors that inhibit the expression or activities of Cas proteins. Whereas most anti-CRISPRs described to date are proteins, recently described small RNAs called RNA anti-CRISPRs (rAcrs) have sequence homology to CRISPR RNAs (crRNAs) and displace them from cognate Cas nucleases. In this work, we report the discovery of rAcrVIA1-a plasmid-encoded small RNA that inhibits the RNA-targeting CRISPR-Cas13 system in its natural host, Listeria seeligeri. We solved the cryo-electron microscopy structure of the Cas13-rAcr complex, which revealed that rAcrVIA1 adopts a fold nearly identical to crRNA despite sharing negligible sequence similarity. Collectively, our findings expand the diversity of rAcrs and reveal an example of immune antagonism through RNA structural mimicry.