  We construct Nielsen-Olesen vortex solution in the noncommutative abelian
Higgs model. We derive the quantized topological flux of the vortex solution.
We find that the flux is integral by explicit computation in the large $\theta$
limit as well as in the small $\theta$ limit. In the context of a tachyon
vortex on the brane-antibrane system we demonstrate that it is this topological
charge that gives rise to the RR charge of the resulting BPS D-brane. We also
consider the left-right-symmetric gauge theory which does not have a
commutative limit and construct an exact vortex solution in it.
