We present a classification scheme for quantum entanglement based on topological links. This is done by identifying a nonrigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the particle, and associating linked rings to entangled particles. This analogy naturally leads us to a classification of multipartite quantum entanglement based on all possible distinct links for any given number of rings. We demonstrate the use of this new classification scheme for three and four qubits, and introduce a new class of states inspired by topological symmetries of links.