We investigate the influence of cosmic magnetic fields on gravitational wav
e perturbations and find exact solutions on large scales. We show that a la
rge-scale magnetic field can generate large-scale non-decaying gravitationa
l waves. In the general case where gravitational waves are generated by oth
er mechanisms, a large-scale magnetic field introduces a new decaying tenso
r mode and modifies the non-decaying mode. The direct effect of the magneti
c field is to damp the gravitational waves, while an indirect magneto-curva
ture effect can either damp or boost the waves. A magnetic field also leads
to a breaking of statistical isotropy, and the magnetic imprint on the ten
sor spectrum in principle provides a means of detecting a primordial field.