If the adsorption results in a measurble decrease in the amount of free DNA in the solution, then you could separate the nanoparticles from the supernatant by centrifugation or filtration and measure the residual free DNA by its 260 nm UV absorbance. The amount adsorbed is the difference between the original supernatant concentration before the nanoparticles were added and the final supernatant concentration, times the volume.