We analyze the global carbon cycle response to a set of stratospheric aerosol injection (SAI) simulations performed by the CESM2(WACCM6‐MA) model. The simulations are performed under the specified SSP2‐4.5 CO2 concentration pathway. It is found that both the temperature stabilization target and the SO2 injection strategy have important effects on the global carbon sink. Relative to the SSP2‐4.5 scenario, averaged over the last 20 years of our simulations (year 2050–2069), simultaneous multi‐location SO2 injection causes an increase in cumulative land carbon uptake of 45 and 23 PgC, and an increase in cumulative ocean carbon uptake of 6 and 2 PgC for temperature stabilization targets of 0.5°C and 1.5°C respectively. For a temperature stabilization target of 1.0°C, SO2 injections increase land and ocean carbon sinks by 22–42 PgC and 4–7 PgC, respectively, depending on the strategies of SO2 injections (low latitude, mid‐to‐high latitude, and multi‐objective injection). Relative to SSP2‐4.5, by year 2069, SAI increases diagnosed cumulative CO2 emissions by 25–53 PgC (3%–6%), implying a decrease in atmospheric CO2 if SO2 injections were performed under a prescribed CO2 emission pathway. Stratospheric SO2 injections slow permafrost thaw, but do not restore permafrost to the previous extent at the same warming level for all injection strategies. An abrupt termination of SO2 injection weakens both the ocean and land carbon sink, and causes a rapid decline of permafrost extent. A gradual phaseout of SO2 injection slows sharp decline of permafrost and delays the rebound of carbon sink.