Graphene's adhesive and charge delocalization properties offer the opportunity for the direct study of biological molecule in the nanoscale regime. The inherent charge on DNA base pairs and the associated phosphate backbone can be probed by non-covalent interactions with graphene, which is a useful platform for the creation of anisotropic nanopatterned biological assemblies. Here, we report the graphene nanoribbon (GNR) supported anisotropic supramolecular self-assembly of single stranded adenine (A), cytosine (C), guanine (G), thymine (T), AT, and GC 20mer oligonucleotides, as well as the unique ordering of double stranded plasmid (circular) and Herring sperm (linear) DNA. The GNRs serve as a double sided adhesive platform for attachment to the SiO2 substrate, as well as DNA oligomers and polymers. The self-assembly is attributed to donor-acceptor interactions between DNA and graphene. These findings demonstrate that the DNA-GNR assembly yields a prospective route to novel bio-relevant nanostructures.