A focusing system based on a polycapillary half-lens optic has been successfully tested for transmission and fluorescence micro-X-ray absorption spectroscopy at a third-generation bending-magnet beamline equipped with a non-fixed-exit Si(111) monochromator. The vertical positional variations of the X-ray beam owing to the use of a non-fixed-exit monochromator were shown to pose only a limited problem by using the polycapillary optic. The expected height variation for an EXAFS scan around the Fe K-edge is approximately 200 microm on the lens input side and this was reduced to approximately 1 microm for the focused beam. Beam sizes (FWHM) of 12-16 microm, transmission efficiencies of 25-45% and intensity gain factors, compared with the non-focused beam, of about 2000 were obtained in the 7-14 keV energy range for an incoming beam of 0.5 x 2 mm (vertical x horizontal). As a practical application, an As K-edge micro-XANES study of cucumber root and hypocotyl was performed to determine the As oxidation state in the different plant parts and to identify a possible metabolic conversion by the plant.