Viruses subvert macromolecular pathways in infected host cells to aid in viral gene amplification or to counteract innate immune responses. Roles for host-encoded, noncoding RNAs, including microRNAs, have been found to provide pro- and anti-viral functions. Recently, circular RNAs (circRNAs), that are generated by a nuclear back-splicing mechanism of pre-mRNAs, have been implicated to have roles in DNA virus-infected cells. This study examines the circular RNA landscape in uninfected and hepatitis C virus (HCV)-infected liver cells. Results showed that the abundances of distinct classes of circRNAs were up-regulated or down-regulated in infected cells. Identified circRNAs displayed pro-viral effects. One particular up-regulated circRNA, circPSD3, displayed a very pronounced effect on viral RNA abundances in both hepatitis C virus- and Dengue virus-infected cells. Though circPSD3 has been shown to bind factor eIF4A3 that modulates the cellular nonsense-mediated decay (NMD) pathway, circPSD3 regulates RNA amplification in a pro-viral manner at a post-translational step, while eIF4A3 exhibits the anti-viral property of the NMD pathway. Findings from the global analyses of the circular RNA landscape argue that pro-, and likely, anti-viral functions are executed by circRNAs that modulate viral gene expression as well as host pathways. Because of their long half-lives, circRNAs likely play hitherto unknown, important roles in viral pathogenesis.