Authorship Attribution (AA) is a sub-field of Authorship Analysis and text classification, attributing a text to the correct author among a closed set of potential authors. Since short texts usually contain less information about the author, authorship attribution on short texts is often more challenging than authorship attribution on long texts. Recently, the widespread use of pre-trained language models has greatly improved the accuracy of text classification tasks. In this paper, we propose a model which uses the pre-trained language model BERTweet with capsule networks, to solve the authorship attribution on tweets. BERTweet is the first large-scale domain-specific pre-trained language model for English tweets, which can generate high-quality sentence representations of tweets. We combine BERTweet with capsule networks which are particularly powerful at capturing deep features of sentence representations. Thus, both BERTweet and capsule help us achieve remarkable improvements on AA tasks. We also incorporate user writing styles into our model. We design new architectures of capsule networks which combine multiple capsule layers, for generating representations from tweets and user writing styles, improving prediction accuracy and robustness. Our experimental results show that our BERTweet_Capsule_UWS combination shows the state-of-the-art result on the known tweet AA dataset.