The issue of cyber-attacks against wind farm sensor systems is the focus of this research. A novel method for detecting and estimating the magnitude of such attacks using a discrete-time adaptive observer is presented. The proposed observer is derived by augmenting the filtered measurement equation into the state space model of individual wind turbines. The key contribution of the paper is the development of an adaptive observer that can accurately estimate the attacks. The performance of the observer is evaluated through numerical simulations showing that it is effective in estimating the magnitude of the attacks. The proposed method using a discrete-time adaptive observer should be relevant for real-world settings to improve the security and reliability of wind farm operations.