We demonstrate analytically that, in toroidal plasmas, scattering by drift wave turbulence could lead to appreciable damping of toroidal Alfvén eigenmodes via generation of short-wavelength electron Landau damped kinetic Alfvén waves. A corresponding analytic expression of the damping rate is derived, and found to be, typically, comparable to the linear drive by energetic particles. The implications of this novel mechanism on the transport and heating processes in burning plasmas are also discussed.