  A solution of effective string theory in four dimensions is presented which
admits interpretation of a rotating black cosmic string. It is constructed by
tensoring the three dimensional black hole, extended with the Kalb-Ramond
axion, with a flat direction. The physical interpretation of the solution is
discussed, with special attention on the axion, which is found to play a role
very similar to a Higgs field. Finally, it is pointed out that the solution
represents an exact WZWN $\sigma$ model on the string world sheet, to all
orders in the inverse string tension $\alpha'$.
