Despite the fact that point cloud registration under noisy conditions has recently begun to be tackled by several non-correspondence algorithms, they neither struggle to fuse the global features nor abandon early state estimation during the iterative alignment. To solve the problem, we propose a novel method named R-PCR (recurrent point cloud registration). R-PCR employs a lightweight cross-concatenation module and large receptive network to improve global feature performance. More importantly, it treats the point registration procedure as a high-order Markov decision process and introduces a recurrent neural network for end-to-end optimization. The experiments on indoor and outdoor benchmarks show that R-PCR outperforms state-of-the-art counterparts. The mean average error of rotation and translation of the aligned point cloud pairs are, respectively, reduced by 75% and 66% on the indoor benchmark (ScanObjectNN), and simultaneously by 50% and 37.5% on the outdoor benchmark (AirLoc).