In the existing coding standards, rate control (RC) plays a critical role in optimally allocating bit-rates to each coding unit, for improving rate-distortion performance under the limited bandwidth. However, the existing RC methods are mainly based on traditional distortion metrics, which fail to take the advantage of the emerging DNN based image quality assessment (IQA) metrics. In this paper, we set up the first attempt to achieve IQA score based RC for image compression. Specifically, a novel visualization based score-distortion (VSD) model and ρ-slope model are proposed to explicitly establish the relationship between IQA score and bit-rates. Then, by solving optimal rate-distortion optimization based on the IQA score, we propose a novel RC method for the HEVC standard. The experimental results show that, given the target bit-rates, the proposed RC method can accurately control the bit-rates and generate the compressed images with higher IQA score and better perceptual quality. More importantly, the proposed RC method is evaluated to be effective over two DNN based IQA metrics and four image datasets, exhibiting the potential in practical use. The code is available at https://github.com/Ffangqy/IQA-RC.