Abstract In this work, we numerically investigate the transport properties of a square lattice built from disordered deoxyribonucleic acid sequence. To do so, we used an effective tight-binding model to describe the electronic structure, while the current is obtained within a Green’s function framework. We show that the self-assembled DNA structures based-on the disordered sequences display currents, which, by increasing the size of the systems, quickly go to undetectable experimental current values.