The rapid advancement of generative AI has enabled the creation of highly photorealistic visual content, offering practical substitutes for real images and videos in scenarios where acquiring real data is difficult or expensive. However, reliably substituting real visual content with AI-generated counterparts requires robust assessment of the perceived realness of AI-generated visual content, a challenging task due to its inherent subjective nature. To address this, we conducted a comprehensive human study evaluating the perceptual realness of both real and AI-generated images, resulting in a new dataset, containing images paired with subjective realness scores, introduced as RAISE in this paper. Further, we develop and train multiple models on RAISE to establish baselines for realness prediction. Our experimental results demonstrate that features derived from deep foundation vision models can effectively capture the subjective realness. RAISE thus provides a valuable resource for developing robust, objective models of perceptual realness assessment.