It is presented an exact solution of straight spinning cosmic strings in
Brans-Dicke theory of gravitation. The possibility of the existence of closed
timelike curves around these cosmic strings is analyzed. Furthermore, the
stability about the formation of the topological defect discussed here is
checked. It is shown the existence of a suitable choice for the integration
constants in which closed timelike curves are not allowed. We also verify if it
is possible that the obtained spacetime can be the source that describes the
observed rotational curves in some galaxies.Comment: 13 pages, 1 figur