Magnetic fields in cosmic string wakes generate magnetohydrodynamic shock waves. The relativistic charged particles in the wake will get accelerated and emit synchrotron radiation. We assume that the overall magnetic field is homogeneous over the width of the wake. Using a one-zone leptonic model, we obtain the spectrum of synchrotron radiation emitted by these non-thermal relativistic electrons in the wake of a cosmic string. We find that the overall spectrum has a broad peak and spans over a wide range of frequencies due to multiple scattering of the electrons. We found that there are some unidentified sources in different catalogues detected by current all-sky surveys in the frequency range of the synchrotron spectrum we have obtained. We discuss how this can be another signature for cosmic string wakes.