  Cosmic strings are generically predicted in many extensions of the Standard
Model of particle physics. We propose a new avenue for detecting cosmic strings
through their effect on the filamentary structure in the cosmic web. Using
cosmological simulations of the density wake from a cosmic string, we examine a
variety of filament structure probes. We show that the largest effect of the
cosmic string is an overdensity in the filament distribution around the string
wake. The signal from the overdensity is stronger at higher redshift, and more
robust with a wider field. We analyze the spatial distribution of filaments
from a publicly available catalog of filaments built from SDSS galaxies. With
existing data, we find no evidence for the presence of a cosmic string wake
with string tension parameter $G\mu$ above $5\times 10^{-6}$. However, we
project WFIRST will be able to detect a signal from such a wake at the $99\%$
confidence level at redshift $z=2$, with significantly higher confidence and
the possibility of probing lower tensions ($G\mu \sim 10^{-6}$), at $z=10$. The
sensitivity of this method is not competitive with constraints derived from the
CMB. However, it provides an independent discovery channel at low redshift,
which could be a smoking-gun in scenarios where the CMB bound can be weakened.
