Tracking individuals is a vital part of many experiments conducted to understand collective behaviour. Ants are the paradigmatic model system for such experiments but their lack of individually distinguishing visual features and their high colony densities make it extremely difficult to perform reliable racking automatically. Additionally, the wide diversity of their species' appearances makes a generalized approach even harder. In this paper, we propose a data-driven multi-object tracker that, for the first time, employs domain adaptation to achieve the required generalisation. This approach is built upon a joint-detection-and-tracking framework that is extended by a set of domain discriminator modules integrating an adversarial training strategy in addition to the tracking loss. In addition to this novel domain-adaptive tracking framework, we present a new dataset and a benchmark for the ant tracking problem. The dataset contains 57 video sequences with full trajectory annotation, including 30k frames captured from two different ant species moving on different background patterns. It comprises 33 and 24 sequences for source and target domains, respectively. We compare our proposed framework against other domain-adaptive and non-domain-adaptive multi-object tracking baselines using this dataset and show that incorporating domain adaptation at multiple levels of the tracking pipeline yields significant improvements. The code and the dataset are available at https://github.com/chamathabeysinghe/da-tracker.