Twist engineering—the alignment of two-dimensional (2D) crystalline layers with a specific orientation—has led to tremendous success in controlling the charge degree of freedom, particularly in producing correlated and topological electronic phases in moiré crystals1,2. However, although pioneering theoretical efforts have predicted that non-trivial magnetism3–5 and magnons6,7 can be made by twisting 2D magnets, the experimental realization of engineering the spin degree of freedom by twisting remains elusive. Here we fabricate twisted double bilayers of a 2D magnet, namely, chromium triiodide (CrI3), and demonstrate the successful twist engineering of 2D magnetism in them. We identify signatures of a new magnetic ground state that is distinct from those in natural two-layer (2L) and four-layer (4L) CrI3. We show that for a very small twist angle, this emergent magnetism can be well approximated by a weighted linear superposition of those of 2L and 4L CrI3, whereas for a large twist angle, it mostly resembles that of isolated 2L CrI3. However, at an intermediate twist angle, there is a finite net magnetization that cannot be simply inferred from any homogeneous stacking configuration, but emerges because spin frustrations are introduced by competition between ferromagnetic and antiferromagnetic exchange coupling within individual moiré supercells.