AbstractFisheries are supposed to be for the benefit of society, producing food, providing livelihoods and enabling cultural continuity. Biological productivity goals for fish stocks operationalised through Harvest Control Rules (HCRs) are central to contemporary fisheries management. While fisheries policies often state socio‐economic objectives, such as enhancing the livelihoods of coastal communities, those are rarely, if ever, incorporated into operationalised management procedures. The lack of articulation of social objectives and lack of monitoring of social outcomes around HCRs amounts to poor public policy. In this article, we explore the potential for social HCRs (sHCRs) with reference points and agreed predefined actions to make the social dimensions of fisheries explicit. sHCRs cannot cover all social dimensions, so should be considered as one tool within a broader framework of fisheries governance. Moreover, successful sHCRs would require sound deliberative and participatory processes to generate legitimate social objectives, and monitoring and evaluation of fisheries management performance against those objectives. We introduce two potential types of sHCRs, one based on allocation of catch within biological limit reference points, and one for when fishing exceeds biological limit reference points. The application of sHCRs, we argue, can foster accountability and help avoid non‐transparent negotiations on size and distribution of the catch. Our proposal is a call to action for policy makers and fisheries managers to properly integrate social criteria into fisheries governance, and for both biophysical fisheries scientists and social scientists to do better in practical collaboration for methods and knowledge development to support this integration.