  We study the entanglement harvesting phenomenon for static detectors locally
interacting with massless scalar fields in the cosmic string spacetime which is
locally flat but with a conical structure characterized by a deficit angle.
Specifically, three alignments of the detectors with respect to the string,
i.e., parallel and vertical alignments with the detectors on the same side of
the string, and vertical alignment with the detectors on two different sides,
are examined. For the alignments on the same side of the string, we find that
the presence of a cosmic string may either assist or inhibit entanglement
harvesting both in the sense of the entanglement harvested and the
harvesting-achievable range of interdetector separation depending on the
detector-to-string distance, and this is remarkably different from the case of
a locally flat spacetime with a reflecting boundary where the boundary always
enlarges the harvesting-achievable range. For the alignment with detectors on
two different sides of the string, the detectors notably can always harvest
more entanglement than those in flat spacetime without a cosmic string, which
is in sharp contrast to those on the same side. Interestingly, the presence of
a cosmic string enlarges the harvesting-achievable range for the detectors in
vertical alignment only in the vicinity of the string, while it always reduces
the harvesting-achievable range for the detectors in parallel alignment.
