  The vector perturbations induced on the brane by gravitational waves
propagating in the bulk are studied in a cosmological framework. Cosmic
expansion arises from the brane motion in a non-compact five-dimensional
anti-de Sitter spacetime. By solving the vector perturbation equations in the
bulk, for generic initial conditions, we find that they give rise to growing
modes on the brane in the Friedmann-Lema\^{\i}tre era. Among these modes, we
exhibit a class of normalizable perturbations, which are exponentially growing
with respect to conformal time on the brane. The presence of these modes is, at
least, strongly constrained by the current observations of the cosmic microwave
background (CMB). We estimate the anisotropies they induce in the CMB, and
derive quantitative constraints on the allowed amplitude of their primordial
spectrum. Our results provide stringent constraints for all braneworld models
with bulk inflation.
