The increasing adoption of Deep Neural Network (DNN)-based Digital Pre-distortion (DPD) in modern communication systems necessitates efficient hardware implementations. This paper presents DPD-NeuralEngine, an ultra-fast, tiny-area, and power-efficient DPD accelerator based on a Gated Recurrent Unit (GRU) neural network (NN). Leveraging a co-designed software and hardware approach, our 22 nm CMOS implementation operates at 2 GHz, capable of processing I/Q signals up to 250 MSps. Experimental results demonstrate a throughput of 256.5 GOPS and power efficiency of 1.32 TOPS/W with DPD linearization performance measured in Adjacent Channel Power Ratio (ACPR) of -45.3 dBc and Error Vector Magnitude (EVM) of -39.8 dB. To our knowledge, this work represents the first AI-based DPD application-specific integrated circuit (ASIC) accelerator, achieving a power-area efficiency (PAE) of 6.6