A series of recent experimental works on twisted homobilayers have unveiled an abundance of exotic states in this system. Valley-polarized quantum anomalous Hall states have been identified at hole doping of , and the fractional quantum anomalous Hall effect is observed at and . In this Letter, we investigate the electronic properties of AA-stacked twisted bilayer at by -space Hartree-Fock calculations. We identify a series of phases, among which a noteworthy phase is the antiferromagnetic Chern insulator, stabilized by an external electric field. We attribute the existence of this Chern insulator to an antiferromagnetic instability at a topological phase transition between the quantum spin hall phase and a band insulator phase. Our research proposes the potential of realizing a Chern insulator beyond , and contributes fresh perspectives on the interplay between band topology and electron-electron correlations in moiré superlattices.