The magnetostatic field of an infinite rectilinear current placed in the stationary gravitational field of a rotating cosmic string is found. An interesting aspect of this problem is that although the metric is mathematically very simple, its physical meaning is not trivial. It depends only on topological parameters. So, the cosmic string vacuum space–time is locally equivalent to the Minkowski space–time, but not globally. The calculations are so simple that they can easily be shown in the classroom.