Novel compact x-ray sources based on inverse Compton scattering can generate brilliant hard x-rays in a laboratory setting. Their collimated intense beams with tunable well-defined x-ray energies make them well suited for x-ray spectroscopy techniques, which are typically carried out at large facilities. Here, we demonstrate a first x-ray absorption spectroscopy proof-of-principle experiment using an inverse Compton x-ray source with a flux of >10 10 photons/s in <5% bandwidth. We measured x-ray absorption near edge structure and extended x-ray absorption fine structure at the silver K-edge (~25.5 keV) for a series of silver samples. We propose an energy-dispersive geometry specifically adapted to the x-ray beam properties of inverse Compton x-ray sources together with a fast concentration correction method that corrects sample inhomogeneities very effectively. The combination of our setup with the inverse Compton source generates x-ray absorption spectra with high energy resolution in exposure times down to one minute. Our results unravel the great benefit of inverse Compton scattering sources for x-ray absorption techniques in a laboratory environment, especially in the hard x-ray regime, which allows to probe absorption edges of high Z materials. X-ray absorption spectroscopy (XAS) is an element-selective spectroscopic method which can probe the chemical surroundings around an atom of interest. More specifically, this technique can provide fingerprint information about the oxidation state, site symmetry, spin state, and thus is widely used in various research fields. Compared to other common x-ray techniques such as x-ray crystallography, XAS is not limited to crystalline or otherwise ordered samples, but is also applicable to disordered systems in different phases 1. Among XAS, x-ray absorption near-edge structure (XANES) is sensitive to transitions from bound electronic core orbitals to unoccupied electronic orbitals which reveals the electronic structure. In contrast, extended x-ray absorption fine structure (EXAFS) is sensitive to local geometric structures on an atomic scale due to photoelectron interference occuring in this region 2,3. With increasing availability of synchrotron radiation from the 1970s, XAS has become widely applicable to different research fields 4. However, the limited access to and high cost of large-scale synchrotron facilities inhibit the widespread use of XAS as part of standard laboratory workflows on a daily basis. Although these days the performance of XAS implemented with x-ray tubes has greatly improved 5-7 , the low brilliance when using bremsstrahlung results in long acquisition times, restricting its applications to only a few certain samples and research subjects. This limitation can be overcome by recent developments in novel compact x-ray sources based on laserproduced plasma (LPP) 8 , high-harmonic generation (HHG) 9,10 , betatron radiation 11 or inverse Compton scattering (also called Thomson scattering) 12-14. Among them, static or ultrafast XAS has recently been dem...