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Low-latency, low-power portable recurrent neural network (RNN) accelerators offer powerful inference capabilities for real-time applications such as IoT, robotics, and human-machine interaction. We propose a lightweight Gated Recurrent Unit (GRU)-based RNN accelerator called EdgeDRNN that is optimized for low-latency edge RNN inference with batch size of 1. EdgeDRNN adopts the spiking neural network inspired delta network algorithm to exploit temporal sparsity in RNNs. Weights are stored in inexpensive DRAM which enables EdgeDRNN to compute large multi-layer RNNs on the most inexpensive FPGA. The sparse updates reduce DRAM weight memory access by a factor of up to 10x and the delta can be varied dynamically to trade-off between latency and accuracy. EdgeDRNN updates a 5 million parameter 2-layer GRU-RNN in about 0.5ms. It achieves latency comparable with a 92W Nvidia 1080 GPU. It outperforms NVIDIA Jetson Nano, Jetson TX2 and Intel Neural Compute Stick 2 in latency by 5X. For a batch size of 1, EdgeDRNN achieves a mean effective throughput of 20.2GOp/s and a wall plug power efficiency that is over 4X higher than the commercial edge AI platforms.