The task of trajectory data-based user identity linkage (UIL) aims to link users from different platforms with massive historical moving data. Although the existing studies for this task have made great efforts, they overlook a significant fact that a substantial volume of trajectory data are derived from road networks. To fill the gap, we extend the task onto road networks, by developing a novel model entitled UIL-RN (User Identity Linkage on Road Networks). Apart from the inherent sequential features involved in trajectories that have been widely utilized in existing work, the road networks-based topological characteristics are fully explored for better trajectory representation learning in this paper. Specifically, the proposed model consists of the following three main components. (1) To explore the topological characteristics, a graph attention network module namely GAT-TPM is designed to convert trajectories into representation vectors of road segments. (2) A Transformer-based encoder is developed to learn the sequential features of trajectories. (3) A novel matcher is introduced to capture the correlations between users and achieve the final linkage. The extensive experiments conducted on two real-world datasets demonstrate that our proposed model UIL-RN outperforms state-of-the-art methods.