The crystal orientation fabric (COF) in ice cores provides detailed information, such as grain size and distribution and the orientation of the crystals in relation to the large-scale glacier flow. These data are relevant for a profound understanding of the dynamics and deformation history of glaciers and ice sheets. The intrinsic, mechanical anisotropy of the ice crystals causes an anisotropy of the polycrystalline ice of glaciers and affects the velocity of acoustic waves propagating through the ice. Here, we employ such acoustic waves to obtain the seismic anisotropy of ice core samples and compare the results with calculated acoustic velocities derived from COF analyses. These samples originate from an ice core from Rhonegletscher (Rhone Glacier), a temperate glacier in the Swiss Alps. Point-contact transducers transmit ultrasonic P waves with a dominant frequency of 1 MHz into the ice core samples and measure variations in the travel times of these waves for a set of azimuthal angles. In addition, the elasticity tensor is obtained from laboratory-measured COF, and we calculate the associated seismic velocities. We compare these COF-derived velocity profiles with the measured ultrasonic profiles. Especially in the presence of large ice grains, these two methods show significantly different velocities since the ultrasonic measurements examine a limited volume of the ice core, whereas the COF-derived velocities are integrated over larger parts of the core. This discrepancy between the ultrasonic and COF-derived profiles decreases with an increasing number of grains that are available within the sampling volume, and both methods provide consistent results in the presence of a similar amount of grains. We also explore the limitations of ultrasonic measurements and provide suggestions for improving their results. These ultrasonic measurements could be employed continuously along the ice cores. They are suitable to support the COF analyses by bridging the gaps between discrete measurements since these ultrasonic measurements can be acquired within minutes and do not require an extensive preparation of ice samples when using point-contact transducers.