Climate change poses a global challenge to agricultural production and food security, especially in developing countries. In Northeast China, a major grain-producing region, the Maize–Soybean rotation is crucial for sustainable agricultural development. However, previous studies have mainly focused on single crops and lacked attention to soil health and regional scale analysis. This study utilises the APSIM model to predict crop yields and soil organic carbon (SOC) under two Representative Concentration Pathways 4.5 and 8.5 (RCP4.5 and RCP8.5) future climate scenarios in different latitude regions of Northeast China. The result shows that climate change has significant spatial and temporal variations on crop yield and soil organic carbon storage in the Maize–Soybean rotation system. Compared to the baseline (1980–2010), maize yields change from −11.6 to 42.8 kg 10a−1 (RCP4.5) and 7.1 to 39.8 kg 10a−1 (RCP8.5), and soybean yields vary from −13.1 to 3.9 kg 10a−1 (RCP4.5) and −16.2 to −5.6 kg 10a−1 (RCP8.5). SOC increases slowly from 0 to 20 cm and decreases from 20 to 40 cm, resulting in a decrease of 21–334 kg ha−1 10a−1 (RCP4.5) and 26–280 kg ha−1 10a−1 (RCP8.5) in predicted future soil organic carbon storage. PLS-PM results show that future precipitation change has a negative impact on SOC accumulation, and temperature rise in the RCP8.5 scenario has a negative impact on SOC storage. SOC storage is positively correlated with crop yields, and the correlation is stronger under RCP8.5, which has a higher explanation for crop yields changes. Climate change significantly affects crop yields and SOC stocks in the Maize–Soybean rotation system of Northeastern China, especially during extreme weather. Therefore, adaptation strategies should fit local needs, early-maturing regions opt for drought-resistant, early varieties and employ conservation tillage and water-saving methods, while medium and late-maturing areas select late varieties, adjust sowing and enhance fertiliser efficiency.