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Inspired by the observation of the doubly charmed state $T_{cc}$ andfollowing theoretical studies on its spectroscopic parameters, we investigateits magnetic dipole moment assigning it the quantum numbers $J^P=1^+$ and boththe compact diquark-antidiquark and molecular structures in the framework ofthe light-cone QCD. We also calculate the magnetic dipole moment of thetheoretically predicted singly charmed state, $Z_V^{++}$, with two units ofelectric charge and the quantum numbers $J^P=1^-$ in diquark-antidiquarkpicture. The numerical results are obtained as $\mu_{T_{cc}^+-Di}=0.66^{+0.34}_{-0.23}~\mu_N$, $ \mu_{T_{cc}^+-Mol} =0.43^{+0.23}_{-0.22}~\mu_N$ and $\mu_{Z_{V}^{++}} =3.35^{+0.89}_{-0.73} ~\mu_N$. These results may bechecked via other phenomenological approaches. The obtained results may beuseful in exact determinations of the natures of these states.

Magnetic dipole moments of the $T_{cc}^+$ and $Z_V^{++}$ tetraquark states