Soil organic carbon (SOC) plays a pivotal role in the global carbon cycle, impacting climate dynamics and necessitating accurate estimation for sustainable land and agricultural management. While traditional methods of SOC estimation face resolution and accuracy challenges, recent technological solutions harness remote sensing, machine learning, and high-resolution satellite mapping. Graph Neural Networks (GNNs), especially when integrated with positional encoders, can capture complex relationships between soil and climate. Using the LUCAS database, this study compared four GNN operators in the positional encoder framework. Results revealed that the PESAGE and PETransformer models outperformed others in SOC estimation, indicating their potential in capturing the complex relationship between SOC and climate features. Our findings confirm the feasibility of applications of GNN architectures in SOC prediction, establishing a framework for future explorations of this topic with more advanced GNN models.