In the context of the Open Access and Open Science initiatives, Research Data Management becomes relevant and of current interest to researchers, libraries and institutions that contribute to the development of scientific knowledge. Particularly in Astronomy, it is a challenge to convert, standardize, process and arrange large volumes of information and data (estimated in several petabytes), coming from the results of astronomical observations, astronomical catalogs, computational codes, among others, which constitute a fundamental initial part of scientific research (McCray, 2017). Due to this, and the limited studies on this subject, a bibliometric methodology was applied to analyze indexed datasets in the Data Citation Index (Web of Science, Clarivate Analytics) in the Astronomy & Astrophysics category, for the period 2010 - 2019, allowing to identify annual evolution, countries and institutions with higher productivity, main repositories and hosting platforms, use in publications indexed in Web of Science. The analysis was complemented with InCites (Clarivate Analytics) bibliometric tool to determine the linkage of the publications with the datasets and their impact. The results from this study show a substantial increase in the number of indexed datasets provided by institutions in the United States, United Kingdom, Spain and Chile, during the analyzed period. In turn, the publications that cite the main datasets show superior performances in the number of citations and the standardized impact, among other productivity and impact metrics.