Stance detection aims to identify the attitude from an opinion towards a certain target. Despite the significant progress on this task, it is extremely time-consuming and budget-unfriendly to collect sufficient high-quality labeled data for every new target under fully-supervised learning, whereas unlabeled data can be collected easier. Therefore, this paper is devoted to few-shot stance detection and investigating how to achieve satisfactory results in semi-supervised settings. As a target-oriented task, the core idea of semi-supervised few-shot stance detection is to make better use of target-relevant information from labeled and unlabeled data. Therefore, we develop a novel target-aware semi-supervised framework. Specifically, we propose a target-aware contrastive learning objective to learn more distinguishable representations for different targets. Such an objective can be easily applied with or without unlabeled data. Furthermore, to thoroughly exploit the unlabeled data and facilitate the model to learn target-relevant stance features in the opinion content, we explore a simple but effective target-aware consistency regularization combined with a self-training strategy. The experimental results demonstrate that our approach can achieve state-of-the-art performance on multiple benchmark datasets in the few-shot setting.