In this paper, we propose a novel control approach for opinion dynamics on evolving networks. The controls modify the strength of connections in the network, rather than influencing opinions directly, with the overall goal of steering the population toward a target opinion. This requires that the social network remains sufficiently connected, the population does not break into separate opinion clusters, and that the target opinion remains accessible. We present several approaches to address these challenges, considering questions of controllability, instantaneous control, and optimal control. Each of these approaches provides a different view on the complex relationship between opinion and network dynamics and raises interesting questions for future research.