This paper proposes a new wireless sensing system equipped with a movable-antenna (MA) array, which can flexibly adjust the positions of antenna elements to improve sensing performance compared to conventional fixed-position antenna arrays (FPAs). The key contributions include deriving the Cramer-Rao bound (CRB) of the mean square error (MSE) for angle of arrival (AoA) estimation as a function of antenna positions for both 1D and 2D MA arrays. For the 1D case, a globally optimal solution is derived to minimize the CRB of AoA estimation MSE. For the 2D case, the minimum of maximum (min-max) CRBs of estimation MSE for the two AoAs with respect to the horizontal and vertical axes is achieved. In the special case of circular antenna movement regions, an optimal solution is derived under certain numbers of MAs and circle radii. The paper also develops an efficient alternating optimization algorithm to obtain a locally optimal solution for MAs' positions by iteratively optimizing their horizontal and vertical coordinates. Numerical results show that the proposed 1D/2D MA arrays significantly decrease the CRB of AoA estimation MSE and actual MSE compared to conventional uniform linear arrays (ULAs) and uniform planar arrays (UPAs). The steering vectors of the designed 1D/2D MA arrays exhibit low correlation in the angular domain, reducing angle estimation ambiguity. The paper also discusses the performance analysis of the proposed system for general 2D regions and provides insights into the optimal deployment of MAs for minimizing the CRB of AoA estimation.This paper proposes a new wireless sensing system equipped with a movable-antenna (MA) array, which can flexibly adjust the positions of antenna elements to improve sensing performance compared to conventional fixed-position antenna arrays (FPAs). The key contributions include deriving the Cramer-Rao bound (CRB) of the mean square error (MSE) for angle of arrival (AoA) estimation as a function of antenna positions for both 1D and 2D MA arrays. For the 1D case, a globally optimal solution is derived to minimize the CRB of AoA estimation MSE. For the 2D case, the minimum of maximum (min-max) CRBs of estimation MSE for the two AoAs with respect to the horizontal and vertical axes is achieved. In the special case of circular antenna movement regions, an optimal solution is derived under certain numbers of MAs and circle radii. The paper also develops an efficient alternating optimization algorithm to obtain a locally optimal solution for MAs' positions by iteratively optimizing their horizontal and vertical coordinates. Numerical results show that the proposed 1D/2D MA arrays significantly decrease the CRB of AoA estimation MSE and actual MSE compared to conventional uniform linear arrays (ULAs) and uniform planar arrays (UPAs). The steering vectors of the designed 1D/2D MA arrays exhibit low correlation in the angular domain, reducing angle estimation ambiguity. The paper also discusses the performance analysis of the proposed system for general 2D regions and provides insights into the optimal deployment of MAs for minimizing the CRB of AoA estimation.