In this paper, we investigate full-wave computed radar tomography (CRT) using a rubble-pile asteroid model in which a realistic shape (Itokawa) is coupled with a synthetic material composition and structure model. The aim is to show that sparse bistatic radar measurements can distinguish details inside a complex-structured rubble-pile asteroid. The results obtained suggest that distinct local permittivity distribution changes such as surface layers, voids, low-permittivity anomalies, highpermittivity boulders, and cracks can be detected with bistatic CRT, when the total noise level in the data is around -10 dB with respect to the signal amplitude. Moreover, the bistatic measurement set-up improves the robustness of the inversion compared to the monostatic case. Reconstructing the smooth Gaussian background distribution was found to be difficult with the present approach, suggesting that complementary techniques, such as gravimetry, might be needed to improve the reliability of the inference in practice.