Attention-based sequence-to-sequence neural network models learn to jointly align and translate. The quadratic-time attention mechanism is powerful as it is capable of handling arbitrary long- distance reordering, but computationally expensive. In this paper, towards making neural translation both accurate and efficient, we follow the traditional pre-reordering approach to decouple reordering from translation. We add a reordering RNN that shares the input encoder with the decoder. The RNNs are trained jointly with a multi-task loss function and applied sequentially at inference time. The task of the reordering model is to predict the permutation of the input words following the target language word order. After reordering, the attention in the decoder becomes more peaked and monotonic. For reordering, we adopt the Inversion Transduction Grammars (ITG) and propose a transition system to parse input to trees for reordering. We harness the ITG transition system with RNN. With the modeling power of RNN, we achieve superior reordering accuracy without any feature engineering. In experiments, we apply the model to the task of text normalization. Compared to a strong baseline of attention-based RNN, our ITG RNN reordering model can reach the same reordering accuracy with only 1/10 of the training data and is 2.5x faster in decoding.