The emergence of two-dimensional (2D) magnetic crystals and moiré engineering of van der Waals materials has opened the door for devising new magnetic ground states via competing interactions in moiré superlattices. Although a suite of interesting phenomena, including multi-flavor magnetic states, noncollinear magnetic states, moiré magnon bands and magnon networks, has been predicted in twisted bilayer magnetic crystals, nontrivial magnetic ground states have yet to be realized. Here, by utilizing the stacking-dependent interlayer exchange interactions in CrI3, we demonstrate in small-twist-angle CrI3 bilayers a noncollinear magnetic ground state. It consists of antiferromagnetic (AF) and ferromagnetic (FM) domains and is a result of the competing interlayer AF coupling in the monoclinic stacking regions of the moiré superlattice and the energy cost for forming AF-FM domain walls. Above a critical twist angle of ~ 3°, the noncollinear state transitions to a collinear FM ground state. We further show that the noncollinear magnetic state can be controlled by electrical gating through the doping-dependent interlayer AF interaction. Our results demonstrate the possibility of engineering new magnetic ground states in twisted bilayer magnetic crystals, as well as gate-voltage-controllable high-density magnetic memory storage.