Across the social and medical sciences, researchers recognize that specifying planned research activities (i.e., 'registration') prior to the commencement of research has benefits for both the transparency and rigour of science. Despite this, evidence suggests that study registrations frequently go unexamined, minimizing their effectiveness. In a way this is no surprise: manually checking registrations against papers is labour- and time-intensive, requiring careful reading across formats and expertise across domains. The advent of AI unlocks new possibilities in facilitating this activity. We present RegCheck, a modular LLM-assisted tool designed to help researchers, reviewers, and editors from across scientific disciplines compare study registrations with their corresponding papers. Importantly, RegCheck keeps human expertise and judgement in the loop by (i) ensuring that users are the ones who determine which features should be compared, and (ii) presenting the most relevant text associated with each feature to the user, facilitating (rather than replacing) human discrepancy judgements. RegCheck also generates shareable reports with unique RegCheck IDs, enabling them to be easily shared and verified by other users. RegCheck is designed to be adaptable across scientific domains, as well as registration and publication formats. In this paper we provide an overview of the motivation, workflow, and design principles of RegCheck, and we discuss its potential as an extensible infrastructure for reproducible science with an example use case.