Target-oriented opinion words extraction (TOWE) is a subtask of aspect-based sentiment analysis (ABSA). It aims to extract the corresponding opinion words for a given opinion target in a review sentence. Intuitively, the relation between an opinion target and an opinion word mostly relies on syntactics. In this study, we design a directed syntactic dependency graph based on a dependency tree to establish a path from the target to candidate opinions. Subsequently, we propose a novel attention-based relational graph convolutional neural network (ARGCN) to exploit syntactic information over dependency graphs. Moreover, to explicitly extract the corresponding opinion words toward the given opinion target, we effectively encode target information in our model with the target-aware representation. Empirical results demonstrate that our model significantly outperforms all of the existing models on four benchmark datasets. Extensive analysis also demonstrates the effectiveness of each component of our models. Our code is available at https://github.com/wcwowwwww/towe-eacl.