Short answer : To the best of my ancient knowledge NO!
Long answer : You can not MEASURE contact angle (CA) with the data coming out of Fourier-Transform Infrared Spectroscopy (FTIR). But you can use it as a justification method for the data that was extracted from CA.
Imagine you performed some sort of Hydrogen/Oxygen treatment on a surface. From CA, you can observe (and MEASURE!) that contact angel decreases (i.e your surface became more hydrophile) as you intensify the treatment parameters. Then you can find some picks - regarding to H2O and O-H - growing in your FTIR data that confirms the increase of the hydrophilicity of the treated surface(but can not MEASURE any angles!).
As stated above by Ali and Curtis there is only a loose connection between the two measurements. CA is a macroscopic geometry while IR spectroscopy is a microscopic measure of molecular vibrations. The theory behind CA is mostly minimization of the Helmholtz free energy for the interfacial area of a flat surface between a liquid and a surface. While one could imagine connecting that to molecular vibrations it is a long road and I'm not sure the results would ever be quantitative. Then the concept of surface roughness is added in to give contact angles corresponding to observations (superhydrophobic etc.) and at present there is no molecular theory that explains these phenomena in detail.