Using electric and magnetic fields measured by the Magnetospheric Multiscale (MMS) mission, we construct a test-particle simulation of a turbulent magnetic reconnection region to investigate observed ion acceleration. We identify three types of energized ions: (1) ion jets, (2) Speiser-like energized ions—both of which carry significant energy but do not produce a strong energetic (>80 keV) tail in the ion distribution—and (3) a separate but sizable population of ions that are accelerated to significantly higher energies (>80 keV) by the turbulent fields. The majority of ions that undergo energization by the turbulent fields cross the magnetic null plane multiple times. By preferentially energizing these particles, the turbulence creates a separate population of ions that mostly exits in the dawn direction of the magnetotail and forms a high-energy power-law tail in the ion flux-energy distribution. We also find that the highest acceleration energies are limited by the size of the turbulent region (with respect to ion gyroradii). Since turbulence is widespread in astrophysical plasmas and has no a priori limit on scale size, the MMS observations suggest turbulence may have a significant role in particle acceleration.