This paper proposes a new wireless sensing system equipped with a movable-antenna (MA) array, which can adjust the positions of antenna elements to improve sensing performance over conventional fixed-position antenna (FPA) arrays. The authors derive the Cramer-Rao bound (CRB) of the mean square error (MSE) for angle of arrival (AoA) estimation for both one-dimensional (1D) and two-dimensional (2D) MA arrays. For the 1D MA array, a globally optimal solution for the MA positions is derived in closed form to minimize the CRB of AoA estimation MSE. For the 2D MA array, the goal is to minimize the maximum (min-max) CRBs of estimation MSE for the two AoAs with respect to the horizontal and vertical axes. An optimal solution for the MA positions is derived for the special case of a circular antenna movement region. An efficient alternating optimization algorithm is developed to obtain a locally optimal solution for the MA positions. Numerical results demonstrate that the proposed 1D/2D MA arrays significantly reduce the CRB and actual MSE compared to conventional uniform linear arrays (ULAs) and uniform planar arrays (UPAs) with different uniform inter-antenna spacings. Additionally, the steering vectors of the designed 1D/2D MA arrays exhibit low correlation in the angular domain, reducing the ambiguity in angle estimation.This paper proposes a new wireless sensing system equipped with a movable-antenna (MA) array, which can adjust the positions of antenna elements to improve sensing performance over conventional fixed-position antenna (FPA) arrays. The authors derive the Cramer-Rao bound (CRB) of the mean square error (MSE) for angle of arrival (AoA) estimation for both one-dimensional (1D) and two-dimensional (2D) MA arrays. For the 1D MA array, a globally optimal solution for the MA positions is derived in closed form to minimize the CRB of AoA estimation MSE. For the 2D MA array, the goal is to minimize the maximum (min-max) CRBs of estimation MSE for the two AoAs with respect to the horizontal and vertical axes. An optimal solution for the MA positions is derived for the special case of a circular antenna movement region. An efficient alternating optimization algorithm is developed to obtain a locally optimal solution for the MA positions. Numerical results demonstrate that the proposed 1D/2D MA arrays significantly reduce the CRB and actual MSE compared to conventional uniform linear arrays (ULAs) and uniform planar arrays (UPAs) with different uniform inter-antenna spacings. Additionally, the steering vectors of the designed 1D/2D MA arrays exhibit low correlation in the angular domain, reducing the ambiguity in angle estimation.