We used AFM to investigate the interaction of polyelectrolytes such as ssDNA and dsDNA molecules with graphene as a substrate. Graphene is an appropriate substrate due to its planarity, relatively large surfaces that are detectable via an optical microscope, and straightforward identification of the number of layers. We observe that in the absence of the screening ions deposited ssDNA will bind only to the graphene and not to the SiO2 substrate, confirming that the binding energy is mainly due to the pi-pi stacking interaction. Furthermore, deposited ssDNA will map the graphene underlying structure. We also quantify the pi-pi stacking interaction by correlating the amount of deposited DNA with the graphene layer thickness. Our findings agree with reported electrostatic force microscopy (EFM) measurements. Finally, we inspected the suitability of using a graphene as a substrate for DNA origami-based nanostructures.