In this paper, a novel concept for cooperative orbit determination (OD) using inter-spacecraft angle-only measurements is proposed. Different from the conventional cooperative OD that only estimates orbit states, the attitude of the observer spacecraft is considered by incorporating the attitude into the estimated vector. The observability of a two-spacecraft system is analyzed based on the observability matrix. Observability analysis reveals that inter-spacecraft angle-only measurements are inadequate to estimate both the attitude and the orbit states in two-body dynamics. The observability of the two-spacecraft system can be improved by considering high-order gravitational perturbation or executing an attitude maneuver on the observer spacecraft. This is the first time that we present the observability analysis and orbit estimation results for a two-spacecraft system considering attitude uncertainty for the observer. Finally, simulation results demonstrate the effectiveness of the proposed method. The results in this paper can be potentially useful for autonomous managements of a spacecraft constellation and formation.