This paper presents a Gated Recurrent Unit (GRU) based recurrent neural network (RNN) accelerator called EdgeDRNN designed for portable edge computing. EdgeDRNN adopts the spiking neural network inspired delta network algorithm to exploit temporal sparsity in RNNs. It reduces off-chip memory access by a factor of up to 10x with tolerable accuracy loss. Experimental results on a 10 million parameter 2-layer GRURNN, with weights stored in DRAM, show that EdgeDRNN computes them in under 0.5 ms. With 2.42 W wall plug power on an entry level USB powered FPGA board, 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 6X. For a batch size of 1, EdgeDRNN achieves a mean effective throughput of 20.2 GOp/s and a wall plug power efficiency that is over 4X higher than all other platforms.