  A large-scale cosmic magnetic field affects not only the growth of density
perturbations, but also rotational instabilities and anisotropic deformation in
the density distribution. We give a fully relativistic treatment of all these
effects, incorporating the magneto-curvature coupling that arises in a
relativistic approach. We show that this coupling produces a small enhancement
of the growing mode on superhorizon scales. The magnetic field generates new
nonadiabatic constant and decaying modes, as well as nonadiabatic corrections
to the standard growing and decaying modes. Magnetized isocurvature
perturbations are purely decaying on superhorizon scales. On subhorizon scales
before recombination, magnetized density perturbations propagate as
magneto-sonic waves, leading to a small decrease in the spacing of acoustic
peaks. Fluctuations in the field direction induce scale-dependent vorticity,
and generate precession in the rotational vector. On small scales, magnetized
density vortices propagate as Alfv\'{e}n waves during the radiation era. After
recombination, they decay slower than non-magnetized vortices. Magnetic
fluctuations are also an active source of anisotropic distortion in the density
distribution. We derive the evolution equations for this distortion, and find a
particular growing solution.
