Polymer biomolecule hybrids represent a powerful class of highly customizable nanomaterials. Here, we report star-polymer conjugates with DNA using a "ligandless" Cu(I) promoted azide-alkyne cycloaddition click reaction. The multivalency of the star-polymer architecture allows for the concomitant conjugation of other molecules along with the DNA, and the conjugation method provides control over the DNA orientation. The star-polymer DNA nanoparticles are shown to assemble into higher-order nanoassemblies through hybridization. Further, we show that the DNA strands can be utilized in controlled disassembly of the nanostructures.