  We show that a magnetic line defect on the surface of a topological insulator
generically supports two distinct branches of spin-polarized and current
carrying one-dimensional bound states. We identify the components of magnetic
scattering that lead to the bound states. The velocity, and hence spin texture,
of each of those branches can be independently tuned by a magnetic field
rotated in the plane of the surface. We compute the local net and spin-resolved
density of states as well as spin accumulation and charge currents. The net
spin polarization and current due to both bound and scattering states vary
stepwise as a function of the electrostatic and magnetic components of the
scattering potential, and can be tuned by an applied field. We discuss
stability of the bound states with respect to impurity scattering.
