We propose a method to measure the time delay of the Five-hundred-meter Aperture Spherical radio Telescope (FAST) using baseband data and periodic noise injection. By applying a sliding time window and calculating the average standard deviation ratio over 1000 noise cycles, high-precision measurement of the noise-induced time delay is achieved. The proposed method offers several advantages, including a short recording duration, high measurement accuracy, and strong immunity to electromagnetic interference. It enables effective monitoring of hardware state changes in the signal chain, and provides technical support for the future participation of the FAST in radio interferometry.