Self-stabilizing protocols can tolerate any type and any number of transient faults. However, in general, self-stabilizing protocols provide no guarantee about their behavior against permanent faults. This paper considers self-stabilizing link-coloring resilient to (permanent) Byzantine faults in arbitrary anonymous networks. First, we show that stabilizing link-coloring is impossible in anonymous cycles when there is no constraint on the spatial scheduling of processes. Then, given the assumption that no correct neighbors execute their actions simultaneously, we present a self-stabilizing link-coloring protocol that is also resilient to Byzantine faults in arbitrary anonymous networks. The protocol uses 2d-1 colors where d is the maximum degree in the network. This protocol guarantees that any link (u, v) between non faulty processes u and v is assigned a color within 2d+2 rounds and its color remains unchanged thereafter. Our protocol is Byzantine insensitive in the sense that the subsystem of correct processes remains operating properly in spite of unbounded Byzantine faults.