  We address the homogenization of the two-dimensional Dirac operator with
position-dependent mass. The mass is piecewise constant and supported on small
pairwise disjoint inclusions evenly distributed along an $\varepsilon$-periodic
square lattice. Under rather general assumptions on geometry of these
inclusions we prove that the corresponding family of Dirac operators converges
as $\varepsilon\to 0$ in the norm resolvent sense to the Dirac operator with a
constant effective mass provided the masses in the inclusions are adjusted to
the scaling of the geometry. We also estimate the speed of this convergence in
terms of the scaling rates.
