Incomplete motional averaging of chemical shift anisotropy upon weak alignment of nucleic acids and proteins in a magnetic field results in small changes in chemical shift. Knowledge of nucleus-specific chemical shift (CS) tensor magnitudes and orientations is necessary to take full advantage of these measurements in biomolecular structure determination. We report the determination by liquid crystal NMR of the CS tensors for all ribose carbons in A-form helical RNA, using a series of novel 3D NMR pulse sequences for accurate and resolved measurement of the ribose C-13 chemical shifts. The orientation of the riboses relative to the rhombic alignment tensor of the molecule studied, a stem-loop sequence corresponding to helix-35 of 23S rRNA, is known from an extensive set of residual dipolar couplings (RDC), previously used to refine its structure. Singular-value-decomposition fits of the chemical shift changes to this structure, or alternatively to a database of helical RNA X-ray structures, provide the CS tensor for each type of carbon. Quantum chemical calculations complement the experimental results and confirm that the most shielded tensor component lies approximately along the local carbon-oxygen bond axis in all cases and that shielding anisotropy for C3' and C4' is much larger than for C1' and C2', with C5' being intermediate.