Recently, growing studies have demonstrated that circular RNAs (circRNAs) function as critical players in multiple human tumors, including papillary thyroid carcinoma (PTC). However, the expression and underlying potential mechanism of circRNAs in PTC are still not fully elucidated. In this study, 14 candidate differentially expressed circRNAs (DECs) between normal thyroid tissues and benign thyroid tissues or PTC were first screened using the GSE93522 dataset by the GEO2R online tool. Then, the structural loop graphs of these 14 circRNAs were obtained through the CSCD database. After performing miRNA co-prediction by combination of CSCD and CRI databases, a potential circRNA-miRNA sub-network, consisting of 9 circRNAs and 21 miRNAs, was successfully constructed. Subsequently, the expression and prognostic values of these miRNAs were further determined by starBase, and two miRNAs, namely, miR-605-5p and miR-876-3p, were identified as key miRNAs in PTC. Then, their downstream target genes were predicted by the miRNet database. CTNNB1 and CCND1 were found to be two most potential targets of miR-876-3p by combination of multiple in silico analyses, including protein–protein interaction (PPI), hub gene screening, correlation analysis, and expression analysis. Conclusively, we established a key hsa_circ_0088494-miR-876-3p-CTNNB1/CCND1 axis linked to carcinogenesis and progression of PTC, which may provide promising therapeutic targets in treating PTC in the future.