Over-the-air computation (AirComp) has emerged as a promising technology for fast wireless data aggregation by harnessing the superposition property of wireless multiple-access channels. This paper investigates a fluid antenna (FA) array-enhanced AirComp system, employing the new degrees of freedom achieved by antenna movements. Specifically, we jointly optimize the transceiver design and antenna position vector (APV) to minimize the mean squared error (MSE) between target and estimated function values. To tackle the resulting highly non-convex problem, we adopt an alternating optimization technique to decompose it into three subproblems. These subproblems are then iteratively solved until convergence, leading to a locally optimal solution. Numerical results show that FA arrays with the proposed transceiver and APV design significantly outperform the traditional fixed-position antenna arrays in terms of MSE.