We experimentally demonstrate reordering throughout the inside of an individual bipolar nematic liquid-crystalline microdroplet optically trapped by a highly focused laser beam, when the laser powers are above a definite threshold. The threshold depends on the droplet size and laser polarization. A physical interpretation of the results is presented by considering the nonlocal orientations of the nematic liquid-crystal molecules in the droplets with the dimensions on the order of the focal spot diameter or larger. On the basis of the finite size approximation, we show that the dependence of threshold power on the droplet size is calculated to be in qualitative agreement with the experimental data.