Cyclic polymer have attracted interest due to their different self-assembly behavior and physical properties compared to their linear counterparts with the same molecular weight. There are only a few examples of using polymer made by RAFT to create cyclic polymers, and no reports of coupling these cyclic polymers together to form stars. In this work, we have demonstrated a novel approach to produce cyclic polymers by RAFT with the required functionality for further coupling to form 2- and 3-arm stars. Cyclization of a chemically modified linear RAFT polystyrene (PSTY) using the copper-catalyzed azide–alkyne cycloaddition (CuAAC) gave cyclic polystyrene (cPSTY) with a purity of 95% as determined by simulating the experimental molecular weight distribution using the log-normal distribution method. The –OH group on cPSTY was converted to an azide via a two step procedure, allowing the cyclic polymers to be coupled together using propargyl ether or tripropargylamine via the CuAAC reaction to form the 2- and 3-arm stars, respectively. When the conventional ligand complex and solvent was used (i.e. CuBr–PMDETA in toluene), the linkage between the cyclic arms degraded fully after 24 h due to base cleavage. We overcame this by changing the ligand to a triazole or carrying out the reaction in ligand-free conditions (i.e. CuBr in DMF). These latter experimental conditions gave ‘click’ efficiencies of greater than 82%. Our methodology for producing cyclic polymers by RAFT will not only extend the range of cyclic polymer by the ring closure method but allow one to utilize these cyclic polymers as building blocks in the formation of more complex polymer architectures.