In this paper we present TweetNLP, an integrated platform for Natural Language Processing (NLP) in social media. TweetNLP supports a diverse set of NLP tasks, including generic focus areas such as sentiment analysis and named entity recognition, as well as social media-specific tasks such as emoji prediction and offensive language identification. Task-specific systems are powered by reasonably-sized Transformer-based language models specialized on social media text (in particular, Twitter) which can be run without the need for dedicated hardware or cloud services. The main contributions of TweetNLP are: (1) an integrated Python library for a modern toolkit supporting social media analysis using our various task-specific models adapted to the social domain; (2) an interactive online demo for codeless experimentation using our models; and (3) a tutorial covering a wide variety of typical social media applications.