  We show that the existence of cosmic strings can be strongly constrained by
the next generation of gravitational lensing surveys at radio frequencies. We
focus on cosmic string loops, which simulations suggest would be far more
numerous than long (horizon-sized) strings. Using simple models of the loop
population and minimal assumptions about the lensing cross section per loop, we
estimate the optical depth to lensing and show that extant radio surveys such
as CLASS have already ruled out a portion of the cosmic string model parameter
space. Future radio interferometers, such as LOFAR and especially SKA, may
constrain $G\mu/c^2 < 10^{-9}$ in some regions of parameter space,
outperforming current constraints from pulsar timing and the CMB by up to two
orders of magnitude. This method relies on direct detections of cosmic strings,
and so is less sensitive to the theoretical uncertainties in string network
evolution that weaken other constraints.
