A microwave-photonics method has been developed for measuring distributed acoustic signals. This method uses microwave-modulated low coherence light as a probe to interrogate distributed in-fiber interferometers, which are used to measure acoustic-induced strain. By sweeping the microwave frequency at a constant rate, the acoustic signals are encoded into the complex microwave spectrum. The microwave spectrum is transformed into the joint time-frequency domain and further processed to obtain the distributed acoustic signals. The method is first evaluated using an intrinsic Fabry Perot interferometer (IFPI). Acoustic signals of frequency up to 15.6 kHz were detected. The method was further demonstrated using an array of in-fiber weak reflectors and an external Michelson interferometer. Two piezo-ceramic cylinders (PCCs) driven at frequencies of 1700 Hz and 3430 Hz were used as acoustic sources. The experiment results show that the sensing system can locate multiple acoustic sources. The system resolves 20 nε when the spatial resolution is 5 cm. The recovered acoustic signals match the excitation signals in frequency, amplitude, and phase, indicating an excellent potential for distributed acoustic sensing (DAS).