In recent years, recommender systems play a pivotal role in helping users identify the most suitable items that satisfy personal preferences. As user-item interactions can be naturally modelled as graph-structured data, variants of graph convolutional networks (GCNs) have become a well-established building block in the latest recommenders. Due to the wide utilization of sensitive user profile data, existing recommendation paradigms are likely to expose users to the threat of privacy breach, and GCN-based recommenders are no exception. Apart from the leakage of raw user data, the fragility of current recommenders under inference attacks offers malicious attackers a backdoor to estimate users' private attributes via their behavioral footprints and the recommendation results. However, little attention has been paid to developing recommender systems that can defend such attribute inference attacks, and existing works achieve attack resistance by either sacrificing considerable recommendation accuracy or only covering specific attack models or protected information. In our paper, we propose GERAI, a novel differentially private graph convolutional network to address such limitations. Specifically, in GERAI, we bind the information perturbation mechanism in differential privacy with the recommendation capability of graph convolutional networks. Furthermore, based on local differential privacy and functional mechanism, we innovatively devise a dual-stage encryption paradigm to simultaneously enforce privacy guarantee on users' sensitive features and the model optimization process. Extensive experiments show the superiority of GERAI in terms of its resistance to attribute inference attacks and recommendation effectiveness.