A synthetic strand of RNA has been designed so that it can adopt two different topological states (a circle and a trefoil knot) when ligated into a cyclic molecule. The RNA knot and circle have been characterized by their behavior in gel electrophoresis and sedimentation experiments. This system allows one to assay for the existence of an RNA topoisomerase, because the two RNA molecules can be inter-converted only by a strand passage event. We find that the interconversion of these two species can be catalyzed by Escherichia coli DNA topoisomerase III, indicating that this enzyme can act as an RNA topoisomerase. The conversion of circles to knots is accompanied by a small amount of RNA catenane generation. These findings suggest that strand passage must be considered a potential component of the folding and modification of RNA structures.