The circular carbon economy is receiving increasing research attention as an essential tool for reducing carbon emissions and mitigating climate change. However, there is no research on the literature distribution and the current situation of the circular carbon economy studies. This paper presents a scientometric analysis of 1452 academic papers on the circular carbon economy and their references from 2010–2021 using the Citespace visualization network. The results show that research on the circular carbon economy has experienced a relatively gradual growth from 2010 to 2016, followed by an explosive growth from 2016 to 2021. Research cooperation among countries is close, forming a relatively concentrated cooperation network, while the core author group has not yet formed. Furthermore, the research on circular carbon economy strongly correlates with relevant international hotspots and national policy changes, reflecting the instrumental characteristics of circular carbon economy research. We summarized three main research topics through keywords clustering. In addition, we point out the future research directions from technical progress considering industry differences and cooperation, multiple environmental policies and legal system construction, interregional and international cooperation, etc., from an institutional research perspective. This article provides an essential and valuable reference for related research.