The synthesis of cyclic amphiphilic graft copolymers with a hydrophobic polycarbonate backbone and hydrophilic poly(N-acryloylmorpholine) (PNAM) side arms via a combination of ring-opening polymerization (ROP), cyclization via copper-catalyzed azide–alkyne cycloaddition (CuAAC), and reversible addition–fragmentation chain transfer (RAFT) polymerization is reported. The ability of these cyclic graft copolymers to form unimolecular micelles in water is explored using a combination of light scattering, small-angle X-ray scattering (SAXS), and cryogenic transmission electron microscopy (cryoTEM) analyses, where particle size was found to increase with increasing PNAM arm length. Further analysis revealed differences in the solution conformations, loading capabilities, and morphologies of the cyclic graft copolymers in comparison to equivalent linear graft copolymer unimolecular micelle analogues. Furthermore, the cyclic and linear graft copolymers were found to exhibit significantly different cloud point temperatures. This study highlights how subtle changes in polymer architecture (linear graft copolymer versus cyclic graft copolymer) can dramatically influence a polymer’s nanostructure and its properties.