We study vorticity production in isothermal, subsonic, acoustic (nonvortical), and decaying turbulence due to the presence of magnetic fields. Using three-dimensional numerical simulations, we find that the resulting kinetic energy cascade follows the ordinary Kolmogorov phenomenology involving a constant spectral energy flux. The nondimensional prefactor for acoustic turbulence is larger than the standard Kolmogorov constant due to the inefficient dissipation of kinetic energy. We also find that the Lorentz force can drive vortical motions even when the initial field is uniform by converting a fraction of the acoustic energy into vortical energy. This conversion is shown to be quadratic in the magnetic field strength and linear in the acoustic flow speed. By contrast, the direct production of vortical motions by a non-force-free magnetic field is linear in the field strength. Our results suggest that magnetic fields play a crucial role in vorticity production in cosmological flows, particularly in scenarios where significant acoustic turbulence is prevalent. We also discuss the implications of our findings for the early Universe, where magnetic fields may convert acoustic turbulence generated during cosmological phase transitions into vortical turbulence.