Precise rotational positioning of end-effectors under microscopy is crucial for robotic micromanipulation. However, the end-effector is presently limited to a fixed orientation, which is manually set before a given micromanipulation task, lacking accuracy and versatility of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> reorientation. In this article, we present a unified framework for rotationally positioning the end-effector in three dimensions by establishing a general rotational model, developing a detection method within the limited field of view under microscopy, and designing a three-loop control strategy that adapts to different experimental requirements and model parameters. In experiments, a standard angled micropipette was used as the end-effector to verify the validity of the proposed methods. The performance was evaluated experimentally where the micropipette was robotically rotated to an arbitrarily desired orientation with an average orientation error less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2^\circ$</tex-math></inline-formula> . In the experiments of sperm manipulation, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> micropipette orientation control capability improved the success rate of sperm immobilization and achieved dexterous robotic sperm orientation for facile aspiration.