Social Networks represent one of the most important online sources to share content across a world-scale audience. In this context, predicting whether a post will have any impact in terms of engagement is of crucial importance to drive the profitable exploitation of these media. In the literature, several studies address this issue by leveraging direct features of the posts, typically related to the textual content and the user publishing it. In this paper, we argue that the rise of engagement is also related to another key component, which is the semantic connection among posts published by users in social media. Hence, we propose TweetGage, a Graph Neural Network solution to predict the user engagement based on a novel graph-based model that represents the relationships among posts. To validate our proposal, we focus on the Twitter platform and perform a thorough experimental campaign providing evidence of its quality.