  We unravel some peculiar properties of ultralong-range Rydberg molecules
formed by an $s$-state $^{87}$Rb Rydberg atom and a corresponding ground-state
atom whose electronic orbitals are spherically symmetric and therefore should
not be influenced by the presence of weak magnetic fields. However, the
electron-atom interaction, which establishes the molecular bond, is under
certain conditions subject to a sizeable spin-orbit coupling and, hence,
sensitive to the magnetic field. This mechanism can be harnessed to
counterintuitively align the $s$-state molecules with respect to the field
axis. We demonstrate this by analyzing the angular-dependent Born-Oppenheimer
potential energy surfaces and the supported vibrational molecular states. Our
predictions open novel possibilities to access the physics of relativistic
electron-atom scattering experimentally.
