As people spend increasingly more time on social networks, cyberbullying has become a social problem that needs to be solved by machine learning methods. Our research focuses on textual cyberbullying detection because text is the most common form of social media. However, the content information in social media is short, noisy, and unstructured with incorrect spellings and symbols, and this impacts the performance of some traditional machine learning methods based on vocabulary knowledge. For this reason, we propose a Char-CNN (Character-level Convolutional Neural Network) model to identify whether the text in social media contains cyberbullying. We use characters as the smallest unit of learning, enabling the model to overcome spelling errors and intentional obfuscation in real-world corpora.