In this paper, we design a geometric stochastic feedback controller to almost globally asymptotically stabilize the rigid body attitude in probability. The attitude motion is represented on the tangent bundle of SO(3) and is subject to an stochastic input torque with an unknown multiplicative diffusion coefficient. In addition, we assume that the variance parameter of the stochastic input torque is unknown. We, first, interpret the attitude dynamics in the Ito sense and the Frobenius norm of the unknown diffusion coefficient is approximated by an unknown bounded scalar parameter. An adaptive backstepping method and a suitable Morse-Lyapunov (M-L) function candidate is then employed to obtain a nonlinear continuous stochastic feedback control law. The almost global asymptotic stability of system is guaranteed in probability and the control gain matrix is obtained through solving LMI feasibility problem. A simulation example is performed to demonstrate the effectiveness of the proposed control scheme on TSO(3).