  Fast magnetic reconnection may occur in different astrophysical sources,
producing flare-like emission and particle acceleration. Currently, this
process is being studied as an efficient mechanism to accelerate particles via
a first-order Fermi process. In this work we analyse the acceleration rate and
the energy distribution of test particles injected in three-dimensional
magnetohydrodynamical (MHD) domains with large-scale current sheets where
reconnection is made fast by the presence of turbulence. We study the
dependence of the particle acceleration time with the relevant parameters of
the embedded turbulence, i.e., the Alfv\'en speed $V_{\rm A}$, the injection
power $P_{\rm inj}$ and scale $k_{\rm inj}$ ($k_{\rm inj} = 1/l_{\rm inj}$). We
find that the acceleration time follows a power-law dependence with the
particle kinetic energy: $t_{acc} \propto E^{\alpha}$, with $0.2 < \alpha <
0.6$ for a vast range of values of $c / V_{\rm A} \sim 20 - 1000$. The
acceleration time decreases with the Alfv\'en speed (and therefore with the
reconnection velocity) as expected, having an approximate dependence $t_{acc}
\propto (V_{\rm A} / c)^{-\kappa}$, with $\kappa \sim 2.1- 2.4$ for particles
reaching kinetic energies between $1 - 100 \, m_p c^2$, respectively.
Furthermore, we find that the acceleration time is only weakly dependent on the
$P_{\rm inj}$ and $l_{\rm inj}$ parameters of the turbulence. The particle
spectrum develops a high-energy tail which can be fitted by a hard power-law
already in the early times of the acceleration, in consistency with the results
of kinetic studies of particle acceleration by magnetic reconnection in
collisionless plasmas.
