Traditional methods for synthesizing single-site catalysts are typically complicated and require special chemicals due to their tendency to agglomerate. In this study, we present a self-disperse copper-based catalyst synthesized via a dry mixing method for acetylene hydrochlorination. During the reaction, the copper precursor compounds, i.e., CuBr, and CuI, were converted to CuCl. Subsequently, the formed CuCl crystals underwent a significant structural transformation, leading to the formation of small clusters and Cu single sites. The catalytic activity of 5% CuCl + C prepared through the dry mixing method decreased from 93.7% to 92.9% after 100 h of reaction under the condition of GHSV (C2H2) = 60 mL·h−1·g−1. A comparison of the 5% CuCl + C with the 5% CuCl/C obtained by the impregnation method reveals that the catalytic stability of the former was higher than the one prepared by the conventional impregnation method. The exceptional catalytic performance can be attributed to the reaction-induced active sites being highly dispersed and the porous structure of activated carbon being maximally preserved, which was confirmed by HAADF-STEM, BET, TPR, and TG. The reaction-induced dispersion of CuCl on carbon provides a new strategy for preparing single-site catalysts for acetylene hydrochlorination.