  We show that the S/F/S Josephson $\varphi_0$-junction permits detection of
macroscopic quantum tunneling and quantum oscillation of the magnetic moment by
measuring the ac voltage across the junction. Exact expression for the tunnel
splitting renormalized by the interaction with the superconducting order
parameter is obtained. It is demonstrated that magnetic tunneling may become
frozen at a sufficiently large $\varphi_0$. The quality factor of quantum
oscillations of the magnetic moment due to finite Ohmic resistance of the
junction is computed. It is shown that magnetic tunneling rate in the
$\varphi_0$-junction can be controled by the supercurrent, with no need for the
magnetic field.
