Contact tracing is an effective public health policy to put the fast-spreading epidemic under control. The government tracks the contacts of confirmed SARS-CoV-2 cases, recommends testing, encourages self-quarantine, and monitors symptoms of contacts. In developing and less-developed countries with limited resources for widespread SARS-CoV-2 testing, it remains essential to identify and quarantine positive contacts to control outbreaks. Therefore, analysing recall and precision when implementing testing policies for these contacts is necessary. We analysed a contact tracing dataset from a cohort of 827 index patients infected with SARS-CoV-2 and their 14814 close contacts from Jan 2020 to July 2020 in a province in eastern China. We constructed a network from the data and used a Graph Convolutional Network to predict each contact’s infection status. To the best of our knowledge, this is the first method to use population-based contact tracing data for predicting the infection status using graph neural networks. Despite limited information, our model achieves competitive Area Under the Receiver Operating Characteristic Curve (ROC AUC) compared to hospital-onset scenarios. Based on the risk scores, we propose several contact testing policy adaptations that balance resource efficiency and effective pandemic control.