  We study the $\theta$-vacuum of QCD using two-flavor chiral perturbation
theory ($\chi$PT) in the presence of a uniform, background magnetic field
calculating the magnetic field-dependent free energy density, the topological
density, the topological susceptibility and the fourth cumulant at one-loop
order. We find that the topological susceptibility is enhanced by the magnetic
field while the fourth topological cumulant is diminished at weak fields and
enhanced at larger fields when $\theta=0$. However, in the QCD vacuum with
$\theta\neq 0$, the topological susceptibility can be either monotonically
enhanced or diminished relative to their $\theta$-vacuum values. The fourth
cumulant also exhibits monotonic enhancement or suppression except for regions
of $\theta$ near $0$ and $2\pi$, where it is both diminished and enhanced.
Finally, the topological density is enhanced for all magnetic fields with its
relative shift being identical to the relative shift of the up and down quark
condensates in the $\theta$-vacuum.
