Open-Vocabulary Multi-Object Tracking (OV-MOT) aims to enable approaches to track objects without being limited to a predefined set of categories. Current OV-MOT methods typically rely primarily on instance-level detection and association, often overlooking trajectory information, which is a unique and essential information of tracking tasks. Utilizing trajectory information can enhance association stability and classification accuracy, especially in cases of occlusion and category ambiguity, thereby improving adaptability to novel classes. Thus motivated, in this paper we propose \textbf{TRACT}, an open-vocabulary tracker that leverages trajectory information to improve both object association and classification in OV-MOT. Specially, we introduce \textit{Trajectory Consistency Reinforcement} (\textbf{TCR}) strategy to maintain continuity across frames while tracking. Furthermore, we propose \textbf{TraCLIP}, a plug-and-play trajectory classification module. It integrates \textit{Trajectory Feature Aggregation} (\textbf{TFA}) and \textit{Trajectory Semantic Enrichment} (\textbf{TSE}) strategies to fully leverage trajectory information from visual and language perspectives, respectively. Experiments on the OV-TAO benchmark demonstrate that our approach significantly improves tracking performance, highlighting trajectory information as a valuable asset for OV-MOT.