Abstract Social media is an important arena for policy contestation. Although online social media debates can yield notable power over political processes offline, little research has examined the relationship between policy actors' influence in offline policymaking and social media policy arenas. We explore the relationship between four types of influence: reputational and formal‐institutional influence offline, and broadcasting and boosting influence online. We ask (1) are influential policy actors better able than others to broadcast their own messages on social media? and (2) are they better able than others to boost the broadcasting influence of other policy actors in social media? Using exponential random graph models on survey and Twitter data from the Finnish climate policy domain, we find that actors with high reputational influence in offline policymaking are also influential online, when measuring influence as the ability to broadcast one's own message. The pattern does not hold for those with formal‐institutional influence offline. Additionally, offline influence does not translate to the ability to further shape online influence by making boosting other actors' visibility. Our results suggest that although online influence partially corresponds to influence in policymaking, influence varies across arenas of policy contestation.