We present CrystalTrace, a Monte Carlo raytracing algorithm designed for radiative transfer computations involving ice crystals with both random and preferred orientations in the visible spectral range. The algorithm can operate as a standalone tool to compute relative intensities or scattering phase functions for individual hexagonal prisms with different sizes and aspect ratios. The current version of CrystalTrace does not support diffraction and ice absorption. Integrated into the three-dimensional radiative transfer solver MYSTIC, which is part of the <em>libRadtran</em> library of radiative transfer, CrystalTrace enables multiple-scattering simulations of absolute radiances. It seamlessly extends MYSTIC's macroscopic raytracing down to the microscopic scale of individual ice crystals. By computing single-scattering properties online, CrystalTrace significantly reduces memory requirements and removes the need for precomputed look-up tables, which are also subject to limited angular resolution. As an extension of MYSTIC, CrystalTrace supports efficient simulations of complex, realistic atmospheric scenes, including ice and water clouds, aerosols, molecules, and surface properties. CrystalTrace, integrated with MYSTIC, fills a critical gap by providing a computationally efficient forward radiative transfer simulator for ice clouds containing oriented crystals, thereby enabling retrievals of oriented ice crystal properties from ground-based, airborne, and satellite imaging observations.