Context. R Aqr is a symbiotic binary system consisting of a mira variable, a hot companion with a spectacular jet outflow, and an extended emission line nebula. Because of its proximity to the Sun, this object has been studied in much detail with many types of high resolution imaging and interferometric techniques. We have used R Aqr as test target for the visual camera subsystem ZIMPOL, which is part of the new extreme adaptive optics (AO) instrument SPHERE at the Very Large Telescope (VLT). Aims. We describe SPHERE/ZIMPOL test observations of the R Aqr system taken in Hα and other filters in order to demonstrate the exceptional performance of this high resolution instrument. We compare our observations with data from the Hubble Space Telescope (HST) and illustrate the complementarity of the two instruments. We use our data for a detailed characterization of the inner jet region of R Aqr. Methods. We analyze the high resolution ≈25 mas images from SPHERE/ZIMPOL and determine from the Hα emission the position, size, geometric structure, and line fluxes of the jet source and the clouds in the innermost region <2 (<400 AU) of R Aqr. The data are compared to simultaneous HST line filter observations. The Hα fluxes and the measured sizes of the clouds yield Hα emissivities for many clouds from which one can derive the mean density, mass, recombination time scale, and other cloud parameters. for the "outer" clouds around 300 AU, N e ≈ 3 × 10 6 cm −3 for the "inner" clouds around 50 AU, and even higher for the central jet source. The high N e of the clouds implies short recombination or variability timescales of a year or shorter. Conclusions. Hα high resolution data provide a lot of diagnostic information for the ionized jet gas in R Aqr. Future Hα observations will provide the orientation of the orbital plane of the binary and allow detailed hydrodynamical investigations of this jet outflow and its interaction with the wind of the red giant companion.