The intentional manipulation of public opinion has become prevalent in the realm of computational propaganda. The swift spread of misinformation through social networking sites poses significant challenges for governments and society, impacting various aspects of human life. Arab countries are considered among the most affected countries. Accurately identifying and countering computational propaganda is crucial, especially given the impracticality of manually annotating large volumes of social media-generated data. Moreover, the constant propagandists' evolving tactics pose a challenge to accounting models, making the immediate preparation of responsive training data difficult. To address this issue, this research proposes a novel weakly supervised learning approach, leveraging programmatic labeling to label training data in a systematic and timely manner. New labeling functions (LFs) are introduced, where experts' heuristics, knowledge, new proposed lexicons, different fine-tuned pre-trained models are turned into rules to label the data. Leveraging these LFs, we fine-tune a deep learning model for computational propaganda detection. The proposed model achieves a remarkable 94% accuracy and 86% precision in the minority class, outperforming a fine-tuned, fully supervised deep learning model. This research contributes a substantial dataset, a robust weakly supervised model, and lexicons, offering valuable tools for combating computational propaganda on Arabic social media. The code and the dataset are publicly available at https://github.com/Bmalmotairy/Arabic-Propaganda-Detection.