  A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron,
placed in a weak, static, uniform magnetic field perpendicular to the atomic
plane, is considered. Closed forms of the first- and second-order Zeeman
corrections to energy levels are calculated analytically, within the framework
of the Rayleigh-Schr\"odinger perturbation theory, for an arbitrary electronic
bound state. The second-order calculations are carried out with the use of the
Sturmian expansion of the two-dimensional generalized radial Dirac-Coulomb
Green function derived in the paper. It is found that, in contrast to the case
of the three-dimensional atom [P. Stefa\'nska, Phys. Rev. A 92 (2015) 032504],
in two spatial dimensions atomic magnetizabilities (magnetic susceptibilities)
are expressible in terms of elementary algebraic functions of a nuclear charge
and electron quantum numbers. The problem considered here is related to the
Coulomb impurity problem for graphene in a weak magnetic field.
