In many types of computer simulation, a ring polymer of length l in a particular solvent is represented as a polygon of N sides of length l(p), where N approximate to l/l(p), and l(p) is the persistence length. There are many established methods to make such polygons, including kink-jump, bend-spring, and dimerization. This paper introduces a very efficient and easy-to-program method, called vector shuffling, which is useful for generating such polygons in the important special case where the quality of the solvent is good, and the polymer is said to be under theta conditions.