  We use analytic estimates and numerical simulations of test particles
interacting with magnetohydrodynamic (MHD) turbulence to show that subsonic MHD
turbulence produces efficient second-order Fermi acceleration of relativistic
particles. This acceleration is not well-described by standard quasi-linear
theory but is a consequence of resonance broadening of wave-particle
interactions in MHD turbulence. We provide momentum diffusion coefficients that
can be used for astrophysical and heliospheric applications and discuss the
implications of our results for accretion flows onto black holes. In
particular, we show that particle acceleration by subsonic turbulence in
radiatively inefficient accretion flows can produce a non-thermal tail in the
electron distribution function that is likely important for modeling and
interpreting the emission from low luminosity systems such as Sgr A* and M87.
