We present phonon properties of plutonium metal obtained from a combination of density-functional-theory (DFT) electronic structure and the recently developed compressive sensing lattice dynamics (CSLD). The CSLD model is here trained on DFT total energies of several hundreds of quasi-random atomic configurations for best possible accuracy of the phonon properties. The calculated phonon dispersions compare better with experiment than earlier results obtained from dynamical mean-field theory. The density-functional model of the electronic structure consists of disordered magnetic moments with all relativistic effects and explicit orbital-orbital correlations. The magnetic disorder is approximated in two ways: (i) a special quasi-random structure and (ii) the disordered-local-moment method within the coherent potential approximation. Magnetism in plutonium has been debated intensely, but the present magnetic approach for plutonium is validated by the close agreement between the predicted magnetic form factor and that of recent neutron-scattering experiments.