We develop a method to calculate the configuration-averaged density of phonon modes in a liquid. Our strategy is based on the isomorphism between the calculation of the density of modes of a harmonic structure and the determination of transport properties of a random walker on that structure. The density of modes calculation for a fluid in d dimensions is shown to require solution of a random walk, in which a walker with d internal states moves among sites located at the particles of the fluid. We generalize the random walk theory of Gochanour, Andersen, and Fayer to treat this vector random walk, and use this approach to calculate the averaged density of phonon modes in a Lennard-Jones fluid. The calculation agrees well with Monte Carlo simulation results of Seeley and Keyes.