The sodium salt of the maleic acid-allylpropionate-styrene terpolymer was used for recovery of copper ions from aqueous solution. Effects of contact time, sorbent weight and initial Cu2+ ion concentrations on removal efficiency were tested. The maximum experimental sorption capacity of the sorbent for copper ions is 0.71 g g−1. The sorption isotherm of copper ions onto a prepared polymer sorbent has been studied and the equilibrium data were analyzed using Langmuir and Freundlich isotherm models. The adsorption isotherm data showed that copper ions adsorption on the sorbent was better fitted to the Langmuir isotherm model. The Lagergren pseudo-first- and pseudo-second-order kinetic models were applied to examine the kinetics of the copper ions sorption by the synthesized sorbent. The kinetic data are best described by the pseudo-second-order model. The calculated value of the maximum sorption capacity by the pseudo-second-order equation (0.62 g g−1) corresponds well with its experimentally found value (0.71 g g−1). Considering the obtained kinetic data, and the Fourier transform infrared spectroscopy (FT-IR) and UV-vis spectra of the sorbent after the sorption, it is possible to come to the conclusion that during the sorption process Cu2+ ions enter a complex with the carboxylic groups of the maleic acid units of the sorbent.