Copper smelters generate large amounts of copper smelting dust (CSD) that has a high recycling value because it contains about 20% copper. Waste acid can be used to leach CSD. Here, the effects of different temperatures, times and liquid–solid ratios on copper, iron and arsenic leaching rates were investigated. The optimal conditions were determined to be a temperature of 95°C, leaching time of 3 h, and liquid–solid ratio of 7:1. Under these condition, the leaching rate of copper reached 96.37%, and the copper ion concentration was 32.71 g/L. The leaching kinetics date revealed that the leaching of copper and iron was controlled by two different reaction models. The leaching of copper conformed to the Johnson–Mehl–Avrami (JMA) model and was diffusion controlled, and the reaction was rapid in the first 60 min. In contrast, leaching of iron was controlled by a chemical reaction. Copper and iron activation energies were 2.579 and 62.791 kJ/mol, respectively. These results show that CSD waste acid is can be used to dispose of arsenic‐containing hazardous waste in a green, sustainable, and ecologically method.