  Stimulated by a very recent experiment observing successfully two
superconducting states with even- and odd-number of electrons in a nanowire
topological superconductor as expected from the existence of two end Majorana
quasiparticles (MQs) [Albrecht \textit{et al.}, Nature \textbf{531}, 206
(2016)], we propose a way to manipulate Majorana qubit exploiting quantum
tunneling effects. The prototype setup consists of two one-dimensional (1D)
topological superconductors coupled by a tunneling junction which can be
controlled by gate voltage. We show that, upon current injection, the time
evolution of superconducting phase difference at the junction induces an
oscillation in energy levels of the Majorana parity states, whereas the
level-crossing is avoided by a small coupling energy of MQs in the individual
1D superconductors. This results in a Landau-Zener-St\"{u}ckelberg (LZS)
interference between the Majorana parity states. Adjusting the current pulse
and gate voltage, one can build a LZS interferometry which provides an
arbitrary manipulation of the Majorana qubit. The LZS rotation of Majorana
qubit can be monitored by the microwave radiated from the junction.
