Information about the external wrench in legged robots is crucial for performing interactive tasks. However, most previous research has relied on attaching force/torque sensors to the end-effectors, which has disadvantages in terms of cost and maintenance. Therefore, this article presents a sensorless method for estimating the external wrench on a legged robot. It involves two main steps. First, a nonlinear disturbance observer is used to obtain a noise-reduced ground reaction force estimate. Then, to obtain the applied external wrench value, a factor graph optimization method is implemented to couple the IMU, camera, and estimated leg force data tightly. Unlike the conventional method, the high performance of the optimization approach and the fusion with the exteroceptive sensor improved the estimation accuracy. The effectiveness of the proposed method was verified through several experiments.