Geoengineering techniques such as solar radiation management (SRM) could be part of a future technology portfolio to limit global temperature change. However, there is public opposition to research and deployment of SRM technologies. We use 814,924 English-language tweets containing #geoengineering globally over 13 years (2009–2021) to explore public emotions, perceptions, and attitudes toward SRM using natural language processing, deep learning, and network analysis. We find that specific conspiracy theories influence public reactions toward geoengineering, especially regarding “chemtrails” (whereby airplanes allegedly spray poison or modify weather through contrails). Furthermore, conspiracies tend to spillover, shaping regional debates in the UK, USA, India, and Sweden and connecting with broader political considerations. We also find that positive emotions rise on both the global and country scales following events related to SRM governance, and negative and neutral emotions increase following SRM projects and announcements of experiments. Finally, we also find that online toxicity shapes the breadth of spillover effects, further influencing anti-SRM views.