This paper presents the results from direct numerical simulations of homogeneous ferrofluid turbulence with a spatially uniform, applied oscillating magnetic field. Due to the strong coupling that exists between the magnetic field and the ferrofluid, we find that the oscillating field can affect the characteristics of the turbulent flow. The magnetic field does work on the turbulent flow and typically leads to an increased rate of energy loss via two dissipation modes specific to ferrofluids. However, under certain conditions this magnetic work results in injection, or a forcing, of turbulent kinetic energy into the flow. For the cases considered here, there is no mean shear and the mean components of velocity, vorticity, and particle spin rate are all zero. Thus, the effects shown are entirely due to the interactions between the turbulent fluctuations of the ferrofluid and the magnetic field. In addition to the effects of the oscillation frequency, we also investigate the effects of the choice of magnetization equation. The calculations focus on the approximate centerline conditions of the relatively low Reynolds number turbulent ferrofluid pipe flow experiments described previously [K. R. Schumacher, Phys. Rev. E 67, 026308 (2003)].