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We study the equilibrium dc Josephson current in a junction between an$s$-wave and a topological superconductor. Cooper pairs from the $s$-wavesuperconducting lead can transfer to the topological side either via anunpaired Majorana zero mode localized near the junction, or via the above-gapcontinuum states. We find that the Majorana contribution to the supercurrentcan be switched on when time-reversal symmetry in the conventional lead isbroken, e.g., by an externally applied magnetic field inducing a Zeemansplitting. Moreover, if the magnetic field has a component in the direction ofthe effective spin-orbit field, there will be a Majorana-induced anomaloussupercurrent at zero phase difference. This behavior may serve as a signaturecharacteristic of Majorana zero modes, and is accessible to devices with onlysuperconducting contacts.

Josephson current via an isolated Majorana zero mode