In this paper, the adsorption process of copper ions on activated carbon (AC) was simulated in a column test. It was deduced that it is consistent with the pseudo-second-order model. Cation exchange was observed to be the major mechanism of Cu–AC interactions through scanning electron microscopy–energy dispersive X-ray spectroscopy (SEM–EDS), X-ray diffraction (XRD), and Fourier transform infrared spectroscopy (FTIR) measurements. Adsorption isotherms were fitted well using the Freundlich model. Adsorption thermodynamics at 298, 308, 318 K demonstrated that the adsorption process is spontaneous and endothermic. Spectral induced polarization (SIP) technique was used to monitor the adsorption process, and the double Cole–Cole model was used to analyze the SIP results. The normalized chargeability was proportional to the adsorbed copper content. Two measured relaxation times from the SIP testing were converted into the average pore sizes of 2, 0.8, 0.6, 100–110, 80–90, and 53–60 µm by the Schwartz equation, which are consistent with the measured pore sizes from both mercury intrusion porosimetry and scanning electron microscopy (SEM). The reduction in the pore sizes by SIP during the flow-through tests suggested that the adsorbed Cu2+ gradually migrated into small pores as with continued permeation of the influent. These results showcased the feasibility of using SIP technique in engineering practice involving the monitoring of copper contamination in land near a mine waste dump or in adjacent permeable reactive barriers.