The Earth's solid inner core exhibits a global seismic anisotropy of several percents. It results from a coherent alignment of anisotropic Fe alloy crystals through the inner‐core history that can be sampled by present‐day seismic observations. By combining self‐consistent polycrystal plasticity, inner‐core formation models, Monte‐Carlo search for elastic moduli, and simulations of seismic measurements, we introduce a multiscale model that can reproduce a global seismic anisotropy of several percents aligned with the Earth's rotation axis. Conditions for a successful model are an hexagonal close packed structure for the inner‐core Fe alloy, plastic deformation by pyramidal 〈c + a〉 slip, and large‐scale flow induced by a low‐degree inner‐core formation model. For global anisotropies ranging between 1 and 3%, the elastic anisotropy in the single crystal ranges from 5 to 20% with larger velocities along the c axis.