Fine-structure populations and collision–induced energy transfer in atoms are of interest for many fields, from combustion to astrophysics. In particular, neutral carbon atoms are known to play a role in interstellar media, either as probes of physical conditions (ground state 3Pj spin-orbit populations), or as cooling agent (collisional excitation followed by radiative decay). This work aims at investigating the spin-orbit excitation of atomic carbon in its ground electronic state due to collisions with molecular deuterium, an isotopic variant of H2, the most abundant molecule in the interstellar medium. Spin-orbit excitations of C(3Pj) by H2 or D2 are governed by non-adiabatic and spin-orbit couplings, which make the theoretical treatment challenging, since the Born-Oppenheimer approximation no longer holds. Inelastic collisional cross-sections were determined for the C(3P0) + D2 → C(3Pj) + D2 (with j = 1 and 2) excitation process. Experimental data were acquired in a crossed beam experiment at low collision energies, down to the excitation thresholds (at 16.42 and 43.41 cm−1, respectively). C-atoms were produced mainly in their ground spin-orbit state, 3P0, by dissociation of CO in a dielectric discharge through an Even-Lavie pulsed valve. The C-atom beam was crossed with a D2 beam from a second valve. The state-to-state cross-sections were derived from the C(3Pj) (j = 1 or 2) signal measured as a function of the beam crossing angle, i.e., as a function of the collision energy. The results show different quantum behaviors for excitation to C(3P1) or C(3P2) when C(3P0) collides with ortho-D2 or normal-D2. These experimental results are analyzed and discussed in the light of highly accurate quantum calculations. A good agreement between experimental and theoretical results is found. The present data are compared with those obtained for the C-He and C-H2 collisional systems to get new insights into the dynamics of collision induced spin-orbit excitation/relaxation of atomic carbon.