Estimating rigid body attitude dynamics in the presence of unknown or uncertain torques, has applications to unmanned aerial, ground, (under)water and space vehicles. This work provides a new approach to estimating the attitude states and unknown, time-varying, (disturbance) torque vector acting on a rigid body, using an extended state observer. The observer design uses the concept of geometric homogeneity to obtain its stability. A Lyapunov stability analysis is carried out to prove its stability properties. The resulting observer for the attitude states and disturbance torque is smooth, Hölder-continuous, and exhibits almost globally finite-time stable (AG-FTS) with a constant disturbance torque in body frame. These properties are theoretically shown, and a numerical simulation is carried out to demonstrate how the observer works in a realistic attitude estimation scenario.