Graph Neural Networks have achieved tremendous success in modeling complex graph data in a variety of applications. However, there are limited studies investigating privacy protection in GNNs. In this work, we propose a learning framework that can provide node-level privacy, while incurring low utility loss. We focus on a decentralized notion of Differential Privacy, namely Local Differential Privacy, and apply randomization mechanisms to perturb both feature and label data before being collected by a central server for model training. Specifically, we investigate the application of randomization mechanisms in high-dimensional feature settings and propose an LDP protocol with strict privacy guarantees. Based on frequency estimation in statistical analysis of randomized data, we develop reconstruction methods to approximate features and labels from perturbed data. We also formulate this learning framework to utilize frequency estimates of graph clusters to supervise the training procedure at a sub-graph level. Extensive experiments on real-world and semi-synthetic datasets demonstrate the validity of our proposed model.