The anisotropy of magnetic susceptibility (AMS) is a widely used tool to infer rock fabrics, yet quantitative interpretation is limited by sparse single-crystal magnetic properties for rock-forming minerals and by the difficulty of separating intrinsic diamagnetism from impurity-related magnetism. Here we use density-functional theory (DFT) combined with perturbation theory to compute the diamagnetic susceptibility and AMS of calcite-group carbonates (calcite, magnesite, and dolomite) and to quantify the additional paramagnetic contribution from transition-metal doping. For pure calcite, the calculated susceptibility and its anisotropy are in good agreement with published single-crystal measurements, validating the ab initio approach for diamagnetic phases. We provide improved intrinsic diamagnetic reference values for magnesite and dolomite, for which experimental susceptibilities are commonly affected by magnetic impurities. To address impurity effects explicitly, we model Fe and Mn substitution in calcite using supercells. The computed spin moments reproduce expected high-spin states (Fe²⁺, S=2; Mn²⁺, S=5/2) and yield a susceptibility anisotropy per Fe concentration that matches the experimental slope. The strong anisotropy is primarily governed by an orbital contribution tied to the crystallographic c-axis rather than by spin-orbit coupling, highlighting orbital magnetisation as a key but numerically challenging ingredient for modelling of paramagnetic AMS in carbonates.