Carbon dioxide emissions are the primary and most direct contributor to global warming, posing a significant hazard to both the environment and human health. In response to this challenge, there has been a growing interest in the development of effective carbon capture technologies. This study involved the synthesis of 13-X molecular sieve porous materials using solid waste coal gangue as a source of silicon and aluminum. The synthesis process involved the controlled utilization of an “alkali fusion-hydrothermal” reaction system. The resulting materials were characterized for their structure, morphology, and crystal composition using X-ray diffraction and field emission scanning electron microscopy. These 13-X molecular sieve materials were employed as adsorbents to capture carbon dioxide gas, and their adsorption performance was investigated. The findings indicated that the 13-X molecular sieve materials possess uniform pores and complete crystalline morphologies, and they exhibited an adsorption capacity of 1.82 mmol/g for carbon dioxide at 0 °C. Consequently, this study not only converted solid waste gangue into high-value products but also demonstrated effective atmospheric carbon dioxide capture, suggesting that gangue-based 13-X molecular sieves may serve as a potential candidate for carbon capture.