Graphene quantum dots (GQDs) are an allotrope of carbon with a planar surface amenable to functionalization and nanoscale dimensions that confer photoluminescence. Collectively, these properties render GQDs an advantageous platform for nanobiotechnology applications, including optical biosensing and delivery. Towards this end, noncovalent functionalization offers a route to reversibly modify and preserve the pristine GQD substrate, however, a clear paradigm has yet to be realized. Herein, we demonstrate the feasibility of noncovalent polymer adsorption to GQD surfaces, with a specific focus on single-stranded DNA (ssDNA). We study how GQD oxidation level affects the propensity for polymer adsorption by synthesizing and characterizing four types of GQD substrates ranging ~60-fold in oxidation level, then investigating noncovalent polymer association to these substrates. Adsorption of ssDNA quenches intrinsic GQD fluorescence by 31.5% for low-oxidation GQDs and enables aqueous dispersion of otherwise insoluble no-oxidation GQDs. ssDNA-GQD complexation is confirmed by atomic force microscopy, by inducing ssDNA desorption, and with molecular dynamics simulations. ssDNA is determined to adsorb strongly to no-oxidation GQDs, weakly to low-oxidation GQDs, and not at all for heavily oxidized GQDs. Finally, we reveal the generality of the adsorption platform and assess how the GQD system is tunable by modifying polymer sequence and type