  We study the embedding of cosmic strings, related to the
Abrikosov-Nielsen-Olesen vortex solution, into d=4, N=1 supergravity. We find
that the local cosmic string solution which saturates the BPS bound of
supergravity with $D$-term potential for the Higgs field and with constant
Fayet--Iliopoulos term, has 1/2 of supersymmetry unbroken. We observe an
interesting relation between the gravitino supersymmetry transformation,
positive energy condition and the deficit angle of the cosmic string. We argue
that the string solutions with magnetic flux with F-term potential cannot be
supersymmetric, which leads us to a conjecture that D1-strings (wrapped
D(1+q)-branes) of string theory in the effective 4d supergravity are described
by the D-term strings that we study in this paper. We give various consistency
checks of this conjecture, and show that it highlights some generic properties
of non-BPS string theory backgrounds, such as brane-anti-brane systems.
Supersymmetry breaking by such systems can be viewed as FI D-term breaking,
which implies, under certain conditions, the presence of gauged R-symmetry on
such backgrounds. The D-term nature of the brane-anti-brane energy can also
provide information on the superpotential for the tachyon, which Higgses the
R-symmetry. In this picture, the inter-brane force can be viewed as a result of
the world-volume gauge coupling renormalization by the open string loops.
