Black carbon (BC) aerosols from incomplete combustion generally warm the climate, but the magnitudes of their various interactions with climate are still uncertain. A key knowledge gap is their role as ice nucleating particles (INPs), enabling ice formation in clouds. Here we assess the global radiative impacts of BC acting as INPs, using simulations with the Community Earth System Model 2 climate model updated to include new laboratory‐based ice nucleation parameterizations. Overall, we find a moderate cooling through changes to stratiform cirrus clouds, counteracting the well‐known net warming from BC's direct scattering and absorption of radiation. Our best estimates indicate that BC INPs generally thin cirrus by indirectly inhibiting the freezing of solution aerosol, with a global net radiative impact of −0.13 ± 0.07 W/m2. Sensitivity tests of BC amounts and ice nucleating efficiencies, and uncertainties in the environment where ice crystals form, show a potential range of impacts from −0.30 to +0.02 W/m2.