X-ray diffraction experiments on textured polycrystalline aggregates in the diamond anvil cell can be used to determine the single-crystal elastic properties of the material under high pressure. We describe a direct method to extract the elastic moduli of ϵ-Fe from diffraction data without assumptions used in previous models to evaluate the requirements on measurement precision. Assuming elastic properties and a realistic texture, variations of d-spacings with orientation have been calculated. From these data, and assuming a sufficient precision, it was possible to retrieve the elastic moduli used in input. We establish the feasibility of the method, which is also applicable to other materials. This is important for explaining the discrepancies between the experimental results and those from first-principles calculations. Implications for the seismic anisotropy in the Earth’s inner core are discussed.