We propose an experimental setup to test the role of curved spacetime on entanglement extraction from the vacuum of a quantum field to a pair of artificial atoms. In particular, we consider two superconducting qubits coupled to a dc-SQUID array embedded into an open microwave transmission line, where a suitable external bias is able to mimic a spacetime containing a traversable wormhole. We find that the amount of vacuum entanglement that can be extracted by the superconducting qubits depends on the parameters of the wormhole. At some distances qubits that would remain separable in flat spacetime become entangled due to the presence of the effective wormhole background.