Being able to recommend links between users in online social networks is important both for the platforms themselves and for third parties leveraging social media information to grow their business. Predictions are typically based on unsupervised or supervised learning, often leveraging simple yet effective graph topological information, such as the number of common neighbors. However, we argue that richer information about personal social structure of individuals might lead to better predictions. In this paper, we propose to leverage well-established social cognitive theories to improve link prediction performance. According to these theories, individuals arrange their social relationships along, on average, five concentric circles of decreasing intimacy. We postulate that relationships in different circles have different importance in predicting new links. In order to validate this claim, we focus on popular prediction algorithms (both unsupervised and supervised) and we extend them to include social-circles awareness. We validate the prediction performance of these social-aware algorithms against their baseline versions, leveraging two Twitter datasets comprising a community of video gamers and generic users. We show that social-awareness generally provides significant improvements in the prediction performance. In addition, social-awareness is able to deliver good predictions also in cases where resources (e.g., storage, computing) are limited and other approaches perform poorly. Finally, we show that social-awareness can be used in place of using a classifier (which may be costly or impractical) for targeting a specific category of users.