Several investigators have proposed that compressional wave anisotropy in indurated, deep-sea carbonates is caused by a preferred orientation of calcite c axes normal to bedding. To test this hypothesis, we have used X ray pole figure goniometry to measure calcite fabrics in three goniometry to measure calcite fabrics in three anisotropic, calcareous sediment samples from Deep-Sea Drilling Project hole 516F, on the Rio Grande Rise, Anisotropy in these samples ranges from 3.4 to 12.0%. The suggested concentration from 3.4 to 12.0%. The suggested concentration of c axies is present but very weak; concentrations of c axes normal to bedding are in the range 1.1--1.3% per 1% area. We used the Voigt-Ruess-Hill averaging scheme to calculate velocities from the X ray fabric data and found that even in nonporous, pure carbonate rocks, having the observed concentrations of c axes, the acoustic anisotorpy would be less than 1%. We conclude that preferred orientation of calcite is not a significant contributor to compressional wave anisotropy in deep-sea sediments.