Investigations of single fragile objects manipulated by optical forces with high brilliance X-ray beams may initiate the development of new research fields such as protein crystallography in an aqueous environment. We have developed a dedicated optical tweezers setup with a compact, portable, and versatile geometry for the customary manipulation of objects for synchrotron radiation applications. Objects of a few micrometers up to a few tens of micrometers size can be trapped for extended periods of time. The selection and positioning of single objects out of a batch of many can be performed semi-automatically by software routines. The performance of the setup has been tested by wide-angle and small-angle X-ray scattering experiments on single optically trapped starch granules, using a synchrotron radiation microbeam. We demonstrate here for the first time the feasibility of microdiffraction on optically trapped protein crystals. Starch granules and insulin crystals were repeatedly raster-scanned at about 50 ms exposure/raster-point up to the complete loss of the structural order. Radiation damage in starch granules results in the appearance of low-angle scattering due to the breakdown of the polysaccharide matrix. For insulin crystals, order along the densely packed [110] direction is preferentially maintained until complete loss of long-range order.