What is the optimal design of the international corporate tax system? We revisit this classic question in a multi-country general equilibrium model that incorporates three key features of the modern globalized economy: multinational production; intangible capital; and international profit shifting. Our model’s competitive equilibrium is inefficient due to an externality that arises from international spillovers in intangible investment. In the absence of profit shifting, there is little, if anything, a Ramsey planner can do with corporate income taxes to improve the allocation of intangible investment across countries. However, in the presence of profit shifting, a planner to use corporate income taxes fully internalize the externality and achieve an efficient allocation of intangible investment. To quantitatively investigate the properties of the Ramsey planner’s optimal policy in a more realistic setting, we extend our model to an environment with firm heterogeneity and selection into multinational production. The optimal policy in this environment is to cut corporate income taxes in rich countries and raise taxes in poor countries, which would benefit the latter substantially and shut down profit shifting worldwide. When the planner is constrained to Pareto improvements relative to the status quo, the optimal policy would be more modest and would allow profit shifting to continue to operate at a similar level to the status quo.