Numerical experiments of test particle acceleration are performed using turbulent magnetic and electric fields obtained from direct numerical solutions of the compressible three-dimensional Hall magnetohydrodynamic (MHD) equations. Comparisons are made of the results for the test particle momentum distribution function with and without the Hall term in the MHD solution. Electrons and protons are considered for the test particles at short times before particles leave the simulation box (with length size of the order of a few turbulent correlation lengths). The particles momentum distribution functions develop long tails in a short time. For electrons, no substantial difference it is found between results with and without the Hall term in the MHD solution, while for protons differences are seen in the low momentum part of the distributions. When a background uniform magnetic field (guide field) is added, the particle acceleration is anisotropic. Electrons develop large parallel momentum, while protons develop large perpendicular momentum. A discussion of the basic particle acceleration mechanisms in this system is made.