Short-text classification is a challenging task, due to the sparsity and high dimensionality of the feature space. In this study, we aim to analyze and classify Turkish tweets based on their topics. Social media jargon and the agglutinative structure of the Turkish language makes this classification task even harder. As far as we know, this is the first study that uses a Transformer Encoder for short text classification in Turkish. The model is trained in a weakly supervised manner, where the training data set has been labeled automatically. Our results on the test set, which has been manually labeled, show that performing morphological analysis improves the classification performance of the traditional machine learning algorithms Random Forest, Naive Bayes, and Support Vector Machines. Still, the proposed approach achieves an F-score of 89.3 % outperforming those algorithms by at least 5 points.