Developing interventions that successfully reduce engagement with misinformation on social media is challenging. One intervention that has recently gained great attention is Twitter's Community Notes (previously known as "Birdwatch"). Community Notes is a crowdsourced fact-checking approach that allows users to write textual notes to inform others about potentially misleading posts on Twitter. Yet, empirical evidence regarding its effectiveness in reducing engagement with misinformation on social media is missing. In this paper, we perform a large-scale empirical study to analyze whether the introduction of the Community Notes feature and its roll-out to users in the U. S. and around the world have reduced engagement with misinformation on Twitter in terms of retweet volume and likes. We employ Difference-in-Difference (DiD) models and Regression Discontinuity Design (RDD) to analyze a comprehensive dataset consisting of all fact-checking notes and corresponding source tweets since the launch of Community Notes in early 2021. Although we observe a significant increase in the volume of fact-checks carried out via Community Notes, particularly for tweets from verified users with many followers, we find no evidence that the introduction of Community Notes significantly reduced engagement with misleading tweets on Twitter. Rather, our findings suggest that Community Notes might be too slow to effectively reduce engagement with misinformation in the early (and most viral) stage of diffusion. Our work emphasizes the importance of evaluating fact-checking interventions in the field and offers important implications to enhance crowdsourced fact-checking strategies on social media.