With the growth of the social web, user-generated text data has reached unprecedented sizes. Non-canonical text normalization provides a way to exploit this as a practical source of training data for language processing systems. The state of the art in Turkish text normalization is composed of a token-level pipeline of modules, heavily dependent on external linguistic resources and manually-defined rules. Instead, we propose a fully-automated, context-aware machine translation approach with fewer stages of processing. Experiments with various implementations of our approach show that we are able to surpass the current best-performing system by a large margin.