In conventional federated learning (FL), differential privacy (DP) guarantees can be obtained by injecting additional noise to local model updates before transmitting to the parameter server (PS). In the wireless FL scenario, we show that the privacy of the system can be boosted by exploiting over-the-air computation (OAC) and anonymizing the transmitting devices. In OAC, devices transmit their model updates simultaneously and in an uncoded fashion, resulting in a much more efficient use of the available spectrum. We further exploit OAC to provide anonymity for the transmitting devices. The proposed approach improves the performance of private wireless FL by reducing the amount of noise that must be injected.