We develop a discounting rule for estimating the social cost of carbon (SCC) given uncertain economic growth. Diminishing marginal utility of income implies a relationship between the discount rate term structure and economic growth uncertainty. In the classic Ramsey framework, this relationship is governed by parameters reflecting pure time preference and the elasticity of the marginal utility of consumption, yet disagreement remains about the values of these parameters. We calibrate these parameters to match empirical evidence on both the future interest rate term structure and economic growth uncertainty, while also maintaining consistency with discount rates used for shorter-term benefit-cost analysis. Such an integrated approach is crucial amid growth uncertainty, where growth is also a key determinant of climate damages. This results in an empirically driven, stochastic discounting rule to be used in estimating the SCC that also accounts for the correlation between climate damage estimates and discount rates.