Modern technologies for recycling electronic waste (e-waste) have high economic efficiency and environmental safety requirements. Among the existing technologies, hydrometallurgy is considered to be the most promising technology for e-waste recycling. Increasing attention paid to the chlorination method is associated with the complex recycling of low-grade ores containing noble metals and the raw materials of secondary polymetallic. In this paper, we propose a new scheme for leaching metals from computer printed circuit boards (PCBs) pre-crushed in a disintegrator: The processes of chlorine production and hydrochlorination are implemented in one reactor under the action of an alternating current (AC) of industrial frequency (50 Hz). Three fine fractions of raw material powders with particle size d < 90 µm, d = 90–180 µm, and d = 180–350 µm were used as research objects and the finest fraction of the raw material (d < 90 µm) was studied in more detail. It was found that complete leaching of gold is achieved from fractions of raw materials with a particle size d = 90–180 µm and d = 180–350 µm, containing 277 ppm and 67 ppm of the gold, respectively, at an experiment duration (tex) of 2 h, a current density (i) of 0.66 A·cm−2, and a solid/liquid (S/L) ratio of 8.6 g·L−1. Under the same conditions of the electrochemical leaching process from the fraction of raw materials with a particle size of d < 90 µm and a gold content of 824 ppm, the degree of metal leaching is 80.5%. At the same time, with an increase in particle size in the raw material fractions from d < 90 µm to d = 180–350 µm and a copper content in the raw material from 1.40% to 6.13%, an increase in the degree of its leaching from 81.6% to 95.2%, respectively, is observed. In the framework of the preliminary study presented in this work, for the finest raw material fraction with d < 90 μm the highest gold leaching degree (86.3%) was achieved under the following experimental conditions: tex= 4 h, CHCl = 6 M, i = 0.88 A·cm–2, S/L ratio—8.6 g·L–1 and the highest copper leaching degree (94.2%) was achieved under the following experimental conditions: tex = 2 h, CHCl = 6 M, i = 0.64 A·cm–2, and S/L ratio—2.9 g·L–1.