Precision in optical micromanipulation is critical for non-invasive, non-contact control of objects with light and for using light to measure forces and torques. We demonstrate the control of birefringent objects over three translational directions and three rotational degrees of freedom. Our work trapping and rotating calcite, a unique crystal with no axis of symmetry, extends the positioning abilities of optical tweezers. We trap and levitate a single crystal in linearly polarized light and position it in three rotational directions relative to the polarization. Our model of the torque on the crystals is based on determining the induced polarization and its interaction with the incident electric field. Crystals are shown to rest in equilibrium with their optic axis along the beam axis and one extraordinary axis along the direction of polarization. The calculated equilibrium positions align with our observations of stable trapped calcite.