We show that the magnetization of a thin ferromagnetic (Ga,Mn)As layer can be modulated by picosecond acoustic pulses. In this approach a picosecond strain pulse injected into the structure induces a tilt of the magnetization vector M, followed by the precession of M around its equilibrium orientation. This effect can be understood in terms of changes in magnetocrystalline anisotropy induced by the pulse. A model where only one anisotropy constant is affected by the strain pulse provides a good description of the observed time-dependent response.