In this work, we investigate and characterize graphite electrodes (GE) modified with polymeric films derived from 4-hydroxyphenylacetic acid (4-HPA) and 4-aminobenzoic acid (4-ABA) for the determination of the Pb(II) in water samples by square-wave anodic stripping voltammetry (SWASV). The electropolymerization was carried out in acid and basic medium using cyclic voltammetry (CV). The platform with poly(4-ABA) showed higher sensitivity for Pb(II) detection. Then, we performed the optimization of the electropolymerization parameters of 4-ABA where the better electrochemical responses were obtained at a monomer concentration of 0.25 mM with 25 cycles at 25 mV s−1 in the basic media. The modified electrodes showed a decrease in the CV response in a ferricyanide/ferrocyanide potassium solution, and an increase in the charge transfer resistance (Rct) values is obtained by impedance spectroscopy electrochemistry (EIS). The calibration curve obtained for Pb(II) detection showed a linear range from 50 to 3224 µg L−1, with a limit of detection of 13.7 µg L−1 and a limit of quantification of 45.6 µg L−1. Addition and recovery studies showed levels of 94.5%. No detectable levels of Pb(II) under the established conditions were observed in water samples. Therefore, the investigated sensor using poly(4-ABA) is promising for Pb(II) detection in water samples.