A nonlinear rotation-Camassa-Holm equation, physically depicting the motion of equatorial water waves and having the Coriolis effect, is investigated. Using the viscous approximation tool, we obtain an upper bound estimate about the space derivative of the viscous solution and a high order integrable estimate about the time-space variables. Utilizing these two estimates, we prove that there exist $H^1(\mathbb{R})$ global weak solutions to the rotation-Camassa-Holm model.