As beaconless acquisition tracking and pointing (ATP) uses the same laser beam with communication, and needs no more extra laser equipment, it has advantages in inter-satellite optical communication application which limits weight and power consumption of laser communication terminals. For scenario of low earth orbit inter-satellite optical communication, beaconless ATP of small optical terminals based on intensity modulation and direct detection was studied. The link budget was calculated, and the ATP procedure was designed. The effect of boresight vibration on acquisition time and acquisition probability was analyzed, and the method of residual uncertainty cone calculation was presented. It shows that the maximum laser transmitting power required is 0.135 W, and beaconless acquisition time is 30 s with acquisition probability of 95%, which can meet requirements of low earth orbit inter-satellite optical communication links.