An iterative method to simulate 3D fatigue crack propagation in crystalline materials is proposed and demonstrated on simple test cases. The method relies on the computation of a damage indicator based on plastic activity around the crack tip. By post-processing this quantity after a given loading sequence, local crack direction and growth rate are estimated along the crack path. Dedicated remeshing routines allow the crack to propagate in 3D and the iterative process can continue with the updated crack geometry. Two examples in a BCC single crystal featuring different slip systems demonstrate the crack propagation simulations under cyclic loading over distances comparable to the crystal size and with non-regular crack shapes such as zig-zag crack paths. The effect of transferring plastic fields between propagation steps is also analysed.