We report an efficient algorithm for calculating momentum-space integrals in solid state systems on modern graphics processing units (GPUs). We extend the tetrahedron method by Blöchl et al. to the more general case of the integration of a momentum as well as energy dependent quantity and implement the algorithm based on the CUDA programming framework. We test this method by applying it to a simple example, the calculation of the orbital-resolved density of states. We benchmark our code on the problem of calculating the orbital-resolved density of states in an iron-based superconductor and discuss the design choices made in the implementation. Our algorithm delivers large speedups of up to a factor ∼165 also for moderately sized workloads compared to standard algorithms executed on central processing units (CPUs).