The last decade has seen a dramatic increase in attention from the scholarly communications and research community to open access (OA) and open data practices. These are potentially related because journal publication policies and practices both signal disciplinary norms and provide direct incentives for data sharing and citation. However, there is little research evaluating the data policies of OA journals. In this study we analyse the state of data policies for OA journals by employing random sampling of the Directory of Open Access Journals and Open Journal Systems journal directories and applying a coding framework that integrates both previous studies and emerging taxonomies of data sharing and citation. This study, for the first time, reveals both the low prevalence of data-sharing policies and practices in OA journals, which differs from the previous studies of commercial journals in specific disciplines.