Data quality assessment has become a prominent component in the successful execution of complex data-driven artificial intelligence (AI) software systems. In practice, real-world applications generate huge volumes of data at speeds. These data streams require analysis and preprocessing before being permanently stored or used in a learning task. Therefore, significant attention has been paid to the systematic management and construction of high-quality datasets. Nevertheless, managing voluminous and high-velocity data streams is usually performed manually (i.e. offline), making it an impractical strategy in production environments. To address this challenge, DataOps has emerged to achieve life-cycle automation of data processes using DevOps principles. However, determining the data quality based on a fitness scale constitutes a complex task within the framework of DataOps. This paper presents a novel Data Quality Scoring Operations (DQSOps) framework that yields a quality score for production data in DataOps workflows. The framework incorporates two scoring approaches, an ML prediction-based approach that predicts the data quality score and a standard-based approach that periodically produces the ground-truth scores based on assessing several data quality dimensions. We deploy the DQSOps framework in a real-world industrial use case. The results show that DQSOps achieves significant computational speedup rates compared to the conventional approach of data quality scoring while maintaining high prediction performance.