This paper presents a study of nuclear magnetism in the deformed halo nucleus $^{31}$Ne using the time-odd deformed relativistic Hartree-Bogoliubov theory in continuum (TODRHBc). The study explores how nuclear magnetism affects the binding energy and single-particle spectra of $^{31}$Ne, a deformed halo nucleus with an odd number of neutrons. The results show that nuclear magnetism contributes 0.09 MeV to the total binding energy and causes a splitting of 0-0.2 MeV in the canonical single-particle spectra due to the breaking of Kramers degeneracy. The blocked neutron level in $^{31}$Ne has a dominant p-wave component and is marginally bound, but becomes unbound when nuclear magnetism is ignored. This indicates that nuclear magnetism plays a crucial role in stabilizing the nucleus. The study also reveals that a prolate one-neutron halo is formed around the near-spherical core in $^{31}$Ne. The nucleon current is mainly contributed by the halo, except near the center of the nucleus. A layered structure in the neutron current distribution is observed and studied in detail. The results show that nuclear magnetism significantly influences the neutron current distribution, with the halo providing a dominant contribution to the neutron current in most regions of the nucleus. The study also highlights the importance of considering nuclear magnetism in theoretical predictions for exotic nuclei, as it can change the decay properties and exotic structure of such nuclei. The findings suggest that nuclear magnetism plays a key role in making an unbound orbital bound and a nucleus more stable. The study concludes that the inclusion of nuclear magnetism in the TODRHBc theory is essential for accurately describing the properties of exotic nuclei like $^{31}$Ne.This paper presents a study of nuclear magnetism in the deformed halo nucleus $^{31}$Ne using the time-odd deformed relativistic Hartree-Bogoliubov theory in continuum (TODRHBc). The study explores how nuclear magnetism affects the binding energy and single-particle spectra of $^{31}$Ne, a deformed halo nucleus with an odd number of neutrons. The results show that nuclear magnetism contributes 0.09 MeV to the total binding energy and causes a splitting of 0-0.2 MeV in the canonical single-particle spectra due to the breaking of Kramers degeneracy. The blocked neutron level in $^{31}$Ne has a dominant p-wave component and is marginally bound, but becomes unbound when nuclear magnetism is ignored. This indicates that nuclear magnetism plays a crucial role in stabilizing the nucleus. The study also reveals that a prolate one-neutron halo is formed around the near-spherical core in $^{31}$Ne. The nucleon current is mainly contributed by the halo, except near the center of the nucleus. A layered structure in the neutron current distribution is observed and studied in detail. The results show that nuclear magnetism significantly influences the neutron current distribution, with the halo providing a dominant contribution to the neutron current in most regions of the nucleus. The study also highlights the importance of considering nuclear magnetism in theoretical predictions for exotic nuclei, as it can change the decay properties and exotic structure of such nuclei. The findings suggest that nuclear magnetism plays a key role in making an unbound orbital bound and a nucleus more stable. The study concludes that the inclusion of nuclear magnetism in the TODRHBc theory is essential for accurately describing the properties of exotic nuclei like $^{31}$Ne.