  We use current theoretical estimates for the density of long cosmic strings
to predict the number of strong gravitational lensing events in astronomical
imaging surveys as a function of angular resolution and survey area. We show
that angular resolution is the most important factor, and that interesting
limits on the dimensionless string tension Gmu/c^2 can be obtained by existing
and planned surveys. At the resolution of the Hubble Space Telescope (0.14"),
it is sufficient to survey of order a few square degrees -- well within reach
of the current HST archive -- to probe the regime Gmu/c^2 ~ 10^{-7}. If lensing
by cosmic strings is not detected, such a survey would improve the limit on the
string tension by a factor of two over that available from the cosmic microwave
background. Future high resolution imaging surveys, covering a few hundred
square degrees or more, either from space in the optical or from large-format
radio telescopes on the ground, would be able to further lower this limit to
Gmu/c^2 < 10^{-8}.
