In gyrotropic crystals, an oscillating magnetic field induces a charge response known as the gyrotropic magnetic current. While its conventional origin is attributed to magnetic field modified band energy and shift in the Fermi-surface, a recent study identified an additional spin-driven magnetic displacement contribution. Here, we complete the picture by identifying the orbital counterpart of the magnetic displacement current. Using a density-matrix formulation that incorporates both minimal coupling and spin–Zeeman interactions, we derive the electronic equations of motion in the presence of an oscillating magnetic field and uncover a previously unexplored orbital contribution to the wavepacket velocity. Physically, this contribution arises from the time variation of the magnetic field induced charge polarization. In the low frequency transport regime, this mechanism becomes purely intrinsic. We illustrate this intrinsic gyrotropic current of orbital origin in the PT -symmetric antiferromagnet CuMnAs. We show that the intrinsic gyrotropic magnetic current reverses sign upon Neel vector reversal, establishing it as a direct probe of antiferromagnetic order in CuMnAs and other PT -symmetric antiferromagnets.