Scott and Bruce gave pointers to where tables of absorption coefficients can be found.    These are per-atom, and ignore any fine structure or chemistry effects.  XANES measurements are typically labeled as "arbitrary units" because it is both surprisingly tricky and unnecessary for (most) XANES or EXAFS analysis to actually have an accurate absolute measure of the absorption coefficient (either in mass/area or inverse length). 

We can easily measure XANES features at ~1% of the edge jump.   But to get this signal we've (generally, without loss of generality) sampled the intensity of the X-ray beam with an ion chamber that typically absorbs a few percent of the X-rays upstream of our sample, and an ion chamber downstream of our sample (that might absorb more of the X-rays hitting it).  The beam travels through, and is partially absorbed by, any air paths and other material (plastics, sample containers) as well as our sample.   Typically, the sample attenuates the beam by between a factor of 2 and a factor of 100.  The additional stuff in the beam may attenuate by this much as well. 

We typically take "Current from upstream ion chamber" as I0 (it is NOT the absolute flux hitting the sample) and "Current from downstream ion chamber"  I1 (again, NOT the flux leaving the sample), and call -log(I1/I0) "mu" -- it is not in any real units.

To get the real attenuation (thickness  * absorption coefficient) for the sample, we'd have to take many things (some rather subtle) into account.  And because attenuation is exponential, you actually have to be pretty careful to get this right.  On the other hand, for analyzing XANES and EXAFS we really only care about the change in the absorption coefficient from the element of interest, and are willing to normalize to 1 atom of the absorbing species.   This can be tricky enough, but it means all that other stuff cancels out.    To get the absorption coefficient, you have to divide by the sample thickness (and/or know the sample's density).   But sample thicknesses are typically ~10 microns, and if you think you know the average thickness of a sample to 1% of 10 microns, you must have made a very uniform and precise sample, at least compared to what most people study with EXAFS.

That's not to say it can't be done.  A few people, notably Chris Chantler's group at U Melbourne have made some such measurements.   They're challenging, and most beamlines are not set up to do this easily.