The prevalence of the COVID-19 pandemic in day-to-day life has yielded large amounts of stance detection data on social media sites, as users turn to social media to share their views regarding various issues related to the pandemic, e.g. stay at home mandates and wearing face masks when out in public. We set out to make use of this data by collecting the stance expressed by Twitter users, with respect to topics revolving around the pandemic. We annotate a new stance detection dataset, called COVID-19-Stance. Using this newly annotated dataset, we train several established stance detection models to ascertain a baseline performance for this specific task. To further improve the performance, we employ self-training and domain adaptation approaches to take advantage of large amounts of unlabeled data and existing stance detection datasets. The dataset, code, and other resources are available on GitHub.