We introduce a new method to study the fluid-structure interaction of neutrally-buoyant particles suspended in ambient fluid. The presence of the particle is modeled with an immersed boundary method originally proposed by Uhlmann, later modified by Garcia-Villalba et al. to handle neutrally-buoyant spherical particles. In this contribution we extend the methodology to handle particles of arbitrary shape. The modifications to the existing method can be summarized in: i) tracking the rotation of the particle by means of a quaternion-based formulation; and ii) solving the angular momentum equation of the particle in a body-fixed reference frame. One of the main advantages of the new method compared to existing methods is its simplicity, namely, the new formulation uses no extra term needed for the possible non-overlapping of the center of gravity of the particle and its surface shell. We have validated the new method with several test cases. We have studied the motion of a spheroid in a shear flow at negligible Reynolds number, a case for which there exists an analytical solution. The numerical results are in good agreement with the analytical solution. Since the new method can also be used for solid-to-fluid density ratios larger than 0.5, we have studied the settling of an oblate spheroid in ambient fluid. The results are in good agreement with results of highly accurate spectral element method calculations from the literature. At the time of writing we are running additional test cases. In the talk we will show these and additional cases from the ongoing validation process.