  Spin and charge are the two most important degrees of freedom of electrons.
Their interplay lies at the heart of numerous strongly correlated phenomena
including Hubbard model physics and high temperature superconductivity. Such
interplay for bosons, on the other hand, is largely unexplored in condensed
matter systems. Here we demonstrate a unique realization of the spin-1/2
Bose-Hubbard model through excitons in a semiconducting moir\'e superlattice.
We find evidence of a transient in-plane ferromagnetic (FM-$xy$) order of
exciton spin - here valley pseudospin - around exciton filling $\nu_{ex}$ = 1,
which transitions into a FM-$z$ order both with increasing exciton filling and
a small magnetic field of 10 mT. The phase diagram is different from the
fermion case and is qualitatively captured by a simple phenomenological model,
highlighting the unique consequence of Bose-Einstein statistics. Our study
paves the way for engineering exotic phases of matter from spinor bosons, as
well as for unconventional devices in optics and quantum information science.
