  The satellite galaxy Crater II of the Milky Way is extremely cold and
exceptionally diffuse. These unusual properties are challenging to understand
in the standard model of cold dark matter. We investigate the formation of
Crater II in self-interacting dark matter (SIDM), where dark matter particles
can scatter and thermalize. We conduct a series of controlled N-body
simulations to model the tidal evolution of Crater II, varying the
self-interacting cross section, orbit parameters, and initial stellar
distribution. Dark matter self-interactions lead to halo core formation and the
distribution of stars expands accordingly. A cored SIDM halo also boosts tidal
mass loss, allowing for a high orbit. Our simulations show that SIDM halos with
a $1~{\rm kpc}$ core can simultaneously explain the low stellar velocity
dispersion and the large half-light radius of Crater II, remaining robust to
the initial distribution of stars. For the orbit motivated by the measurements
from Gaia Early Data Release 3, the favored self-interacting cross section is
approximately $60~{\rm cm^2/g}$ on the mass scale of Crater II.
