The quality of statistical machine translation performed with phrase based approaches can be increased by permuting the words in the source sentences in an order which resembles that of the target language. We propose a class of recurrent neural models which exploit source-side dependency syntax features to reorder the words into a target-like order. We evaluate these models on the German-to-English and Italian-to-English language pairs, showing significant improvements over a phrase-based Moses baseline. We also compare with state of the art German-to-English pre-reordering rules, showing that our method obtains similar or better results.