Research on screen content images (SCIs) becomes important as they are increasingly used in multi-device communication applications. In this paper, we present a study on perceptual quality assessment of distorted SCIs subjectively and objectively. We construct a large-scale screen image quality assessment database (SIQAD) consisting of 20 source and 980 distorted SCIs. In order to get the subjective quality scores and investigate, which part (text or picture) contributes more to the overall visual quality, the single stimulus methodology with 11 point numerical scale is employed to obtain three kinds of subjective scores corresponding to the entire, textual, and pictorial regions, respectively. According to the analysis of subjective data, we propose a weighting strategy to account for the correlation among these three kinds of subjective scores. Furthermore, we design an objective metric to measure the visual quality of distorted SCIs by considering the visual difference of textual and pictorial regions. The experimental results demonstrate that the proposed SCI perceptual quality assessment scheme, consisting of the objective metric and the weighting strategy, can achieve better performance than 11 state-of-the-art IQA methods. To the best of our knowledge, the SIQAD is the first large-scale database published for quality evaluation of SCIs, and this research is the first attempt to explore the perceptual quality assessment of distorted SCIs.