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We report an optical fiber tweezer based on high-index material for trapping and optical manipulation of microscale particles in water. The use of a high-index material increases the trapping force with respect to the more common silica, through tighter focusing of light. We demonstrate the potential of this simple and versatile device by trapping and rotating nematic liquid crystal drops. We monitor the rotation of the drop by detecting light modulation observed with the same fiber using backscattered light, which exhibits modulation in intensity due to the rotation of the drop; this further extends the capabilities of the fiber tweezers.