  Majorana Josephson junctions in nanowire systems exhibit a pseudo-$4\pi$
period current-phase relation in the clean limit. In this work, we study how
this current-phase relation responds to a tilted magnetic field in a disordered
Majorana Josephson junction within the Bogoliubov-de Gennes approach. We show
that the tilted magnetic field induces a $\phi_0$ phase shift to the
current-phase relation. Most importantly, we find that this $\phi_0$-junction
behavior is robust even in the presence of disorders.
