A rotary positioning apparatus includes a fixing base, a rotation mechanism, two driving modules and a carrier. The rotation mechanism is disposed on the fixing base, the first driving module is disposed on the fixing base and coupled to the rotation mechanism to drive the rotation mechanism rotating around a first rotation axis relatively to the fixing base. The carrier has plural accommodating slots on a circular-arc surface thereof and is pivoted to the rotation mechanism through a second rotation axis passing through the curvature center of the circular-arc surface and perpendicular to the first rotation axis, on which the curvature center is located. The second driving module is disposed on the rotation mechanism and coupled to the carrier to drive the carrier rotating around the second rotation axis relatively to the rotation mechanism. An automatic pick-and-place system and an operation method using the rotary positioning apparatus are also provided.