In the last decades, many researchers have developed algorithms that estimate the quality of a visual content (videos or images). Among them, one recent trend is the use of texture descriptors. In this paper, we investigate the suitability of using Binarized Statistical Image Features (BSIF), the Local Configuration Pattern (LCP), the Complete Local Binary Pattern (CLBP), and the Local Phase Quantization (LPQ) descriptors to design a referenceless image quality assessment (RIQA) method. These descriptors have been successfully used in computer vision applications, but their use in image quality assessment has not yet been thoroughly investigated. With this goal, we use a framework that extracts the statistics of these descriptors and maps them into quality scores using a regression approach. Results show that many of the descriptors achieve a good accuracy performance, outperforming other state-of-the-art RIQA methods. The framework is simple and reliable.