As Graph Neural Networks (GNNs) become popular, libraries like PyTorch-Geometric (PyG) and Deep Graph Library (DGL) are proposed; these libraries have emerged as the de facto standard for implementing GNNs because they provide graph-oriented APIs and are purposefully designed to manage the inherent sparsity and irregularity in graph structures. However, these libraries show poor scalability on multi-core processors, which under-utilizes the available platform resources and limits the performance. This is because GNN training is a resource-intensive workload with high volume of irregular data accessing, and existing libraries fail to utilize the memory bandwidth efficiently. To address this challenge, we propose ARGO, a novel runtime system for GNN training that offers scalable performance. ARGO exploits multi-processing and core-binding techniques to improve platform resource utilization. We further develop an auto-tuner that searches for the optimal configuration for multi-processing and core-binding. The auto-tuner works automatically, making it completely transparent from the user. Furthermore, the auto-tuner allows ARGO to adapt to various platforms, GNN models, datasets, etc. We evaluate ARGO on two representative GNN models and four widely-used datasets on two platforms. With the proposed autotuner, ARGO is able to select a near-optimal configuration by exploring only 5% of the design space. ARGO speeds up state-of-the-art GNN libraries by up to 5.06x and 4.54x on a four-socket Ice Lake machine with 112 cores and a two-socket Sapphire Rapids machine with 64 cores, respectively. Finally, ARGO can seamlessly integrate into widely-used GNN libraries (e.g., DGL, PyG) with few lines of code and speed up GNN training.