We present a framework for simulating the measurement of seismic anisotropy in a model inner core by computing travel time residuals of synthetic seismic rays propagated through the model. The method is first tested on simple inner core structural models consisting of layers with distinct anisotropy, as often proposed in the literature. Those models are not consistent with geodynamics. Hence, we extend the method to a numerically grown inner core composed of ɛ-Fe with flow generated from an excess of crystallization in the equatorial belt, inducing polycrystalline textures. The global inner core anisotropy is seven times smaller than that of the single-crystal. Compositional stratification amplifies the global anisotropy by 15% while the addition of solidification textures reduces it by a factor of two. As such, and within the tested geodynamical models, no published elastic model of ɛ-Fe at inner core conditions allows one to reproduce the 3% cylindrical anisotropy reported in seismology publications. In addition, our models demonstrate that additional information, such as the depth dependence and the spread of the observed anisotropy is a key for revealing the dynamics and history of the inner core.