Cosmic strings are important remnants of early-Universe phase transitions. We show that they may be probed in a new way with LIGO and future gravitational-wave (GW) detectors. When the GW from compact binary mergers passes by a cosmic string, it is gravitationally lensed and left with a characteristic and detectable signal -- the GW fringe. High-frequency detectors such as aLIGO and Einstein Telescope (ET) are favored in order to observe many numbers of fringe periods. But if they are augmented by mid-frequency detectors such as Atom Interferometer (AI) and Big Bang Observatory (BBO), the broadband ($f \simeq 0.1-1000$ Hz) detections can have significantly better fringe resolutions, hence enhanced sensitivities to the unconstrained parameter space ($G\mu \lesssim 10^{-7}$) of cosmic strings.