This paper presents a methodology to assess the stakeholders’ influence in a research project within the context of responsible research and innovation. The methodology is based on a combination of the multicriteria decision making technique analytic network process and the key areas of responsible research. The method allows ranking and ordering the project’s stakeholders based on their influence upon its responsibility. The purpose of such an assessment is to help research teams to more efficiently devote their limited resources to stakeholder management. The procedure is applied to a case study of the Information and Communication Technology business sector. It is an ongoing project at an early phase of development. Influential stakeholders have been identified first, and have been further classified into groups based on their relative importance. The assessment of their influence has been based on up to 16 different criteria, mainly belonging to the framework of responsible research and innovation. In the case study, the most influential criterion was the Capability to promote public engagement, while Developers were found to be the stakeholders most contributing to the research project responsibility. However, as explained, this is a temporary situation, valid for the current project development situation. It may vary over time as criteria vary in weight and stakeholders vary in influence.