In this paper, we propose a blind image quality assessment (BIQA) method using self-attention and a recurrent neural network (RNN); this approach can effectively capture both local and global information from an input image. The implementation of our constructed deep no-reference (NR) assessment framework does not rely on any convolutional operations. First, the capture step for obtaining locally significant information is performed by a self-attention operation inside a divided window. Second, we design a serialized feature input memory subnetwork to fuse the global features of the image. Finally, all the integrated features are uniformly mapped to the target score. The experimental results obtained on publicly available benchmark IQA databases show that our approach outperforms other state-of-the-art algorithms.