Cognitive Diagnosis (CD) aims to evaluate students' cognitive states based on their interaction data, enabling downstream applications such as exercise recommendation and personalized learning guidance. However, existing methods often struggle with accuracy drops in cross-domain cognitive diagnosis (CDCD), a practical yet challenging task. While some efforts have explored exercise-aspect CDCD, such as crosssubject scenarios, they fail to address the broader dual-aspect nature of CDCD, encompassing both student- and exerciseaspect variations. This diversity creates significant challenges in developing a scenario-agnostic framework. To address these gaps, we propose PromptCD, a simple yet effective framework that leverages soft prompt transfer for cognitive diagnosis. PromptCD is designed to adapt seamlessly across diverse CDCD scenarios, introducing PromptCD-S for student-aspect CDCD and PromptCD-E for exercise-aspect CDCD. Extensive experiments on real-world datasets demonstrate the robustness and effectiveness of PromptCD, consistently achieving superior performance across various CDCD scenarios. Our work offers a unified and generalizable approach to CDCD, advancing both theoretical and practical understanding in this critical domain. The implementation of our framework is publicly available at https://github.com/Publisher-PromptCD/PromptCD.