The purpose of this study was to develop an inexpensive, simple, and highly selective cork-modified carbon paste electrode for the determination of Pb(II) by differential pulse anodic stripping voltammetry (DPASV) and square-wave anodic stripping voltammetry (SWASV). Among the cork–graphite electrodes investigated, the one containing 70% w/w carbon showed the highest sensitivity for the determination of Pb(II) in aqueous solutions. Under SWASV conditions, its linear range and relative standard deviation are equal to 1–25 µM and 1.4%, respectively; the limit of detection complies with the value recommended by the World Health Organization. To optimize the operating conditions, the selectivity and accuracy of the analysis were further investigated by SWASV in acidic media. Finally, the electrode was successfully applied for the determination of Pb(II) in natural water samples, proving to be a sensitive electrochemical sensor that meets the stringent environmental control requirements.