The low-bias current-voltage technique was utilized to study charge transport in single-stranded DNA (ssDNA), assessing the method's effectiveness for future studies aimed at estimating the degree of mutation or DNA damage. In the paper, we showed that charge carrier transfer processes in ssDNA can be precisely monitored using low-bias currents. We used negative differential resistance and the Fowler-Nordheim model to differentiate the charge transport mechanisms observed in a device composed of gold electrode-thiol-ssDNA junctions. It was possible to distinguish the processes at the two junctions (Au/thiol and thiol/DNA) due to their distinct current-voltage characteristics. We observed positive charge carrier tunneling, which we attribute to oxidation and reduction processes in the nucleobases of the ssDNA. Our results suggest that even minor changes in DNA chains can be accurately detected using the described methodology.