  Cosmic strings, as remnants of the symmetry breaking phase in the Early
Universe, may be susceptible to non-local physics. Here we show that the
presence of a Poincar\'e-invariant non-locality -- parametrized by a factor
$\exp(-\Box\ell^2)$ -- regularizes the gravitational field and thereby changes
the properties of spacetime: it is now simply connected and the angle deficit
around the cosmic string becomes a function of the radial distance. Similar
changes occur for the non-local gravitomagnetic field of a rotating cosmic
string, and we translate these mathematical facts into the language of
non-local gravitoelectromagnetism and thereby provide a physical
interpretation. We hope that these insights might prove helpful in the search
for traces of non-local physics in our Universe.
