In this work, a low-cost and rapid electrochemical resistive DNA biosensor based on the current relaxation method is described. A DNA probe, complementary to the specific human papillomavirus type 16 (HPV-16) sequence, was immobilized onto a screen-printed gold electrode. DNA hybridization was detected by applying a potential step of 30 mV to the system, composed of an external capacitor and the modified electrode DNA/gold, for 750 µs and then relaxed back to the OCP, at which point the voltage and current discharging curves are registered for 25 ms. From the discharging curves, the potential and current relaxation were evaluated, and by using Ohm’s law, the charge transfer resistance through the DNA-modified electrode was calculated. The presence of a complementary sequence was detected by the change in resistance when the ssDNA is transformed in dsDNA due to the hybridization event. The target DNA concentration was detected in the range of 5 to 20 nM. The results showed a good fit to the regression equation $\mathsf{\Delta }{R}_{total}\left(\mathsf{\Omega }\right)=2.99 \times \left[\mathrm{DNA}\right]+81.55$, and a detection limit of 2.39 nM was obtained. As the sensing approach uses a direct current, the electronic architecture of the biosensor is simple and allows for the separation of faradic and nonfaradaic contributions. The simple electrochemical resistive biosensor reported here is a good candidate for the point-of-care diagnosis of HPV at a low cost and in a short detection time.