Stance detection is an important task for many applications that analyse or support online political discussions. Common approaches include fine-tuning transformer based models. However, these models require a large amount of labelled data, which might not be available. In this work, we present two different ways to leverage LLM-generated synthetic data to train and improve stance detection agents for online political discussions: first, we show that augmenting a small fine-tuning dataset with synthetic data can improve the performance of the stance detection model. Second, we propose a new active learning method called SQBC based on the "Query-by-Comittee" approach. The key idea is to use LLM-generated synthetic data as an oracle to identify the most informative unlabelled samples, that are selected for manual labelling. Comprehensive experiments show that both ideas can improve the stance detection performance. Curiously, we observed that fine-tuning on actively selected samples can exceed the performance of using the full dataset.