Recurrent neural networks (RNNs) provide excellent performance on applications with sequential data such as speech recognition. On-chip implementation of RNNs is difficult due to the significantly large number of parameters and computations. In this work, we first present a training method for LSTM model for language modeling on Penn Treebank dataset with binary weights and multi-bit activations and then map it onto a fully parallel RRAM array architecture ("XNOR-RRAM"). An energy-efficient XNOR-RRAM array based system for LSTM RNN is implemented and benchmarked on Penn Treebank dataset. Our results show that 4-bit activation precision can provide a near-optimal perplexity of 115.3 with an estimated energy-efficiency of ~27 TOPS/W.