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Circular RNA (circRNA) is a class of RNA molecules that forms a closed loop with their 5′ and 3′ ends covalently bonded. CircRNAs are known to be more stable than linear RNAs, have distinct properties and functions, and are promising biomarkers. Existing methods for assembling circRNAs heavily rely on the annotated transcriptomes, hence exhibiting unsatisfactory accuracy without a high-quality transcriptome. We present TERRACE, a new algorithm for full-length assembly of circRNAs from paired-end total RNA-seq data. TERRACE uses the splice graph as the underlying data structure that organizes the splicing and coverage information. We transform the problem of assembling circRNAs into finding paths that “bridge” the three fragments in the splice graph induced by back-spliced reads. We adopt a definition for optimal bridging paths and a dynamic programming algorithm to calculate such optimal paths. TERRACE features an efficient algorithm to detect back-spliced reads missed by RNA-seq aligners, contributing to its much-improved sensitivity. It also incorporates a new machine-learning approach trained to assign a confidence score to each assembled circRNA, which is shown to be superior to using abundance for scoring. On both simulations and biological data sets, TERRACE consistently outperforms existing methods by a large margin in sensitivity while achieving better or comparable precision. In particular, when the annotations are not provided, TERRACE assembles 123%–413% more correct circRNAs than state-of-the-art methods. TERRACE presents a significant advance in assembling full-length circRNAs from RNA-seq data, and we expect it to be widely used in future research on circRNAs.