A sound source direction-of-arrival (DOA) estimation method for microphone array based on ultra-weak fiber Bragg grating (UW-FBG) distributed acoustic sensor is proposed. The principle of acoustic signal demodulation is introduced, the sound pressure sensitivity and frequency response range of a single UW-FBG microphone are analyzed, and a series linear array with three UW-FBG microphones is designed. Combined with convolutional recurrent neural networks, the DOA estimation method is developed. Log-Mel spectral features and SCOT/PHAT joint weighting generalized cross correlation features are used for DOA estimation. The corresponding system is established and experimentally verified. Results show that the measured sound pressure sensitivity of the UW-FBG microphone is in the range of 0.1032-3.306 rad/Pa within the frequency range of 1000-3000 Hz, and the peak sound pressure sensitivity is about 3.306 rad/Pa. The estimated mean error of 2D DOA estimation is about 2.85°, and the error of 3D DOA estimation is about 5.465°. This method has good application prospects in distributed sound source localization.