This article examines global content governance on social media platforms through the lens of digital constitutionalism, which explores how fundamental rights can be embedded within the socio-technical architecture of digital technologies. It highlights the often-overlooked role of civil society in articulating digital rights and principles. In addition to performing a watchdog function and raising awareness about the human rights implications of digital technologies, we argue that civil society organisations play a constitutionalising role, acting as a bridge between international human rights law and platform governance. Above all, by engaging in global conversations, civil society organisations may facilitate the emergence and dissemination of a set of shared principles and rules. By conducting a semantic network analysis on 44 digital bills of rights that were drafted by civil society organisations and addressed content governance issues, the article aims to identify emerging principles as well as to study their alignment with human rights standards, their relationships, and evolution over time. The findings highlight how civil society initiatives have effectively led to a convergence of expectations around a common set of principles for content moderation, which could both pressure and support platforms and policymakers to strike a balance between freedom of expression and protecting people and democratic institutions from harm and disinformation.