Non-Hermitian wave engineering is a recent and fast-moving field that examines both fundamental and application-oriented phenomena(1-7). One such phenomenon is coherent perfect absorption(8-11)-an effect commonly referred to as 'anti-lasing' because it corresponds to the time-reversed process of coherent emission of radiation at the lasing threshold (where all radiation losses are exactly balanced by the optical gain). Coherent perfect absorbers (CPAs) have been experimentally realized in several setups(10-18), with the notable exception of a CPA in a disordered medium (a medium without engineered structure). Such a 'random CPA' would be the time-reverse of a 'random laser'(19,20), in which light is resonantly enhanced by multiple scattering inside a disorder. Because of the complexity of this scattering process, the light field emitted by a random laser is also spatially complex and not focused like a regular laser beam. Realizing a random CPA (or 'random anti-laser') is therefore challenging because it requires the equivalent of time-reversing such a light field in all its degrees of freedom to create coherent radiation that is perfectly absorbed when impinging on a disordered medium. Here we use microwave technology to build a random anti-laser and demonstrate its ability to absorb suitably engineered incoming radiation fields with near-perfect efficiency. Because our approach to determining these field patterns is based solely on far-field measurements of the scattering properties of a disordered medium, it could be suitable for other applications in which waves need to be perfectly focused, routed or absorbed.