Two femtosecond Ti:sapphire lasers with slightly different repetition rates near 1 GHz are coupled to implement high-speed asynchronous optical sampling. The application of this technique is successfully demonstrated in the field of terahertz time-domain spectroscopy (TDS). A time delay of 1 ns is scanned at a frequency of 5 kHz without moving mechanical parts. Compared with that of conventional TDS schemes based on lock-in detection and moving mirrors, the readout time of integrated resonant THz sensors is reduced by a factor of 20, opening the way for high-throughput THz sensing in marker-free DNA analysis.