Stance detection, as the task of determining the viewpoint of a social media post towards a target as 'favor' or 'against', has been understudied in the challenging yet realistic scenario where there is limited labeled data for a certain target. Our work advances research in few-shot stance detection by introducing SocialPET, a socially informed approach to leveraging language models for the task. Our proposed approach builds on the Pattern Exploiting Training (PET) technique, which addresses classification tasks as cloze questions through the use of language models. To enhance the approach with social awareness, we exploit the social network structure surrounding social media posts. We prove the effectiveness of SocialPET on two stance datasets, Multi-target and P-Stance, outperforming competitive stance detection models as well as the base model, PET, where the labeled instances for the target under study is as few as 100. When we delve into the results, we observe that SocialPET is comparatively strong in identifying instances of the `against' class, where baseline models underperform.