This paper shows how to construct quantum entanglement states of n qubits based on a self-stabilizing token ring algorithm. The entangled states can be applied to the fields of the quantum network, quantum Internet, distributed quantum computing, and quantum cloud. To the best of our knowledge, this is the first attempt to construct quantum entanglement based on the self-stabilizing algorithm. By the quantum circuit implementation based on the IBM Quantum Experience platform, it is demonstrated that the construction indeed can achieve specific n qubit entangled states, which in turn can be used to circulate a token in a quantum network or quantum Internet for building a distributed quantum computing system (DQCS). The built DQCS is fault-tolerant in the sense that it can tolerate transient faults such as occasional errors of entangled quantum states.