We report a technique for the single-shot measurement of single-cycle THz radiation without the need for ultrashort laser pulses. The nonlinear mixing between a narrow linewidth laser and a THz pulse encodes the THz temporal profile into the envelope of a new optical pulse. The preservation of temporal and spectral information in this process enables retrieval of the THz pulse from a standard FROG measurement of the new optical signal. A system has been built which includes a broadband OPA for amplification of the low energy transposed pulse to a level compatible with single-shot FROG methods. The technique should prove essential in the characterization of ultrashort THz pulses that are generated with large shot-to-shot jitter.