A preferred orientation of the anisotropic ice crystals influences the viscosity of the ice bulk and the dynamic behaviour of glaciers and ice sheets. Knowledge about the distribution of crystal anisotropy, to understand its contribution to ice dynamics, is mainly provided by crystal orientation fabric (COF) data from ice cores. However, the developed anisotropic fabric does not only influence the flow behaviour of ice, but also the propagation of seismic waves. Two effects are important: (i) sudden changes in COF lead to englacial reflections and (ii) the anisotropic fabric induces an angle dependency on the seismic velocities and, thus, also recorded traveltimes. A framework is presented here to connect COF data with the elasticity tensor to determine seismic velocities and reflection coefficients for cone and girdle fabrics from ice-core data. We connect the microscopic anisotropy of the crystals with the macroscopic anisotropy of the ice mass, observable with seismic methods. Elasticity tensors for different fabrics are calculated and used to investigate the influence of the anisotropic ice fabric on seismic velocities and reflection coefficients, englacially as well as for the ice-bed contact. Our work, therefore, provides a contribution to remotely determine the state of bulk ice anisotropy.