Magnetization textures in twisted bilayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Cr</mml:mi><mml:msub><mml:mi mathvariant="normal">X</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">X</mml:mi></mml:math> =Br, I)

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