In this paper, we study a new entity linking problem where both the entity mentions and the target entities are within a same social media platform. Compared with traditional entity linking problems that link mentions to a knowledge base, this new problem have less information about the target entities. However, if we can successfully link mentions to entities within a social media platform, we can improve a lot of applications such as comparative study in business intelligence and opinion leader finding. To study this problem, we constructed a dataset called Yelp-EL, where the business mentions in Yelp reviews are linked to their corresponding businesses on the platform. We conducted comprehensive experiments and analysis on this dataset with a learning to rank model that takes different types of features as input, as well as a few state-of-the-art entity linking approaches. Our experimental results show that two types of features that are not available in traditional entity linking: social features and location features, can be very helpful for this task.