In free space optical (FSO) communication, acquisition, tracking and pointing (ATP) is the key technology to maintain a high-quality FSO link. Specifically, the detection of pointing angle deviation greatly affects the performance of ATP, especially under weak receiving power. However, the separated beacon laser beam commonly used in ATP will increase the structural complexity of the terminal such as the size, weight, and power. It is unwanted in some limited applications such as satellite. To improve the pointing accuracy with weak signal in beaconless FSO communication, we propose a delta-sigma enabled beaconless cross-correlation (CCR) method with four-quadrant detectors. In the proposed method, a low-frequency sine analog signal for CCR calculation is modulated into a 1-bit digital signal by delta-sigma modulation and then inserted into the communication data as a training sequence. The root means square error (RMSE) of the pointing angle deviation measurement is 14.17 μrad with the incident optical power of -40 dBm. Compared with the direct intensity method, of which RMSE is 67.61 μrad, the proposed method can effectively improve the pointing accuracy with weak power without a beacon laser in FSO communication.