In this paper, we propose a distributed Alamouti space-time code (DASTC) for two-way relay networks employing a single amplify-and-forward (AF) relay. We first derive closed-form expressions for the approximated average sum-rate of the proposed DASTC scheme. Our analysis is validated by a comparison against the results of Monte-Carlo simulations. Numerical results verify the effectiveness of our proposed scheme over the conventional DASTC with one-way communication.