  Twisted heterostructures of van der Waals materials have received much
attention for their many remarkable properties. Here, we present a
comprehensive theory of the long-range ordered magnetic phases of twisted
bilayer $\alpha$-RuCl$_3$ via a combination of first-principles calculations
and atomistic simulations. While a monolayer exhibits zigzag antiferromagnetic
order with three possible ordering wave vectors, a rich phase diagram is
obtained for moir\'e superlattices as a function of interlayer exchange and
twist angle. For large twist angles, each layer spontaneously picks a single
zigzag ordering wave vector, whereas, for small twist angles, the ground state
involves a combination of all three wave vectors in a complex hexagonal domain
structure. This multi-domain order minimizes the interlayer energy while
enduring the energy cost due to the domain wall formation. Our results indicate
that magnetic frustration due to stacking-dependent interlayer exchange in
moir\'e superlattices can be used to tune the magnetic ground state and enhance
quantum fluctuations in $\alpha$-RuCl$_3$.
