  Motivated by the recent experiment demonstration of stacking dependent
interlayer magnetic interaction [T. Song et al., Nat. Mater. 18, 1298 (2019);
T. Li et al., Nat. Mater. 18, 1303 (2019); W. Chen et al., Science 366, 983
(2019)], we investigate the magnetization textures and the control
possibilities in the moir\'{e} pattern formed of twisted bilayer
two-dimensional (2D) magnets CrX$_3$ (X=Br, I). We find that the stacking
dependent interlayer magnetic interaction results in the formation of periodic
magnetization domains in a long-period moir\'{e} pattern. Magnetization
textures with various topological numbers can be constructed, depending on the
winding of the textures around the domain walls. A uniform external magnetic
field competes with the lateral modulated interlayer magnetic interaction and
can be utilized to tune the magnetization textures.
