The functions of non-coding RNAs usually depend on their 3D structures. Therefore, comparing RNA 3D structures is critical in analyzing their functions. We noticed an interesting phenomenon that two non-coding RNAs may share similar substructures when rotating their sequence order. To the best of our knowledge, no existing RNA 3D structural alignment tools can detect this type of matching. In this article, we defined the RNA 3D structure circular matching problem and developed a software tool named CircularSTAR3D to solve this problem. CircularSTAR3D first uses the conserved stacks (consecutive base pairs with similar 3D structures) in the input RNAs to identify the circular matched internal loops and multiloops. Then it performs a local extension iteratively to obtain the whole circular matched substructures. The computational experiments conducted on a non-redundant RNA structure dataset show that circular matching is ubiquitous. Furthermore, we demonstrated the utility of CircularSTAR3D by detecting the conserved substructures missed by regular alignment tools, including structural motifs and conserved structures between riboswitches and ribozymes from different classes. We anticipate CircularSTAR3D to be a valuable supplement to the existing RNA 3D structural analysis techniques.