A new device, the opto-acoustic parametric amplifier (OAPA), is introduced, which is analogous to an optical parametric amplifier (OPA). The radiation pressure reaction of light on the reflective surface of an acoustic resonator provides nonlinearity similar to the Kerr effect in the OPA. The OAPA can be tuned to operate in two regimes. In the positive gain regime, an acoustic signal is directly amplified. In the negative gain regime, we show that the acoustic resonator can be cooled to the quantum ground state.