How do the rules of interaction influence consensus formation in a social network? In this paper, I analyse procedural influence – a construct that is well-established within the group decision-making research tradition – in the context of networked consensus formation. I argue that interaction procedures regulate the flow of social influence among actors, which, in turn, potentially affects collective outcomes. Based on this, I explain how procedural influence can be integrated into a formal model of social influence. I then utilise an agent-based simulation (ABS) to quantify the effects of three exemplary interaction rules on the formation of consensus in a social network. My findings indicate that applying these rules to regulate interactions has mixed effects on the overall consensus outcomes, but consistently negative effects on the efficiency of consensus formation.