Aims. We aim to study the spatial distribution of the v = 1 and v = 2 J = 1-0 SiO maser emission from R Aqr, a well known stellar symbiotic system. In particular, we intend to determine the annual parallax and proper motion of the source by means of measurements of the absolute coordinates of the maser spots. Methods. We performed VLBI observations of the v = 1 and v = 2 J = 1-0 maser emission, at 7 mm wavelength, using VERA. We present observations made in 11 epochs, between December 2004 and October 2006, and observations by other authors are also discussed. VERA provides very high spatial resolution and accurate astrometric measurements, thanks to its double-beam observing system. From fitting ring-like structures to the maser spot distributions, we determine absolute J2000 coordinates of the central star. (SiO maser emission is known to be distributed around the star forming spot rings at a few stellar radii.) Results. Maps with accurate absolute coordinates were obtained in 8 epochs. From the coordinates determined for the central star, we measured parallax and linear proper motion. We obtain π = 4.7 ± 0.8 mas, compatible with, but much more accurate than, the Hipparcos value (5.07 ± 3.15 mas), and deduce a distance of R Aqr D = 214 +45 -32 pc. Our accurate astrometry also yields a reliable comparison between the spot distributions of both v = 1 and v = 2 J = 1-0 lines. We find that both masers come from similar regions, i.e. at similar distances from the star and defining common spot clusters, confirming previous results. But the coincidences between spots of both lines are very rare, within the spatial and spectral resolution of our experiments. This result is found for eight epochs, spanning more than one pulsation cycle (of the cool Mira-type component). We argue that explaining the finer details of the v = 1,2 J = 1-0 distributions found here would require new theoretical efforts. Finally, our observations also allow the study of the structure and dynamics of the close circumstellar shells in R Aqr. We do not confirm the previous suggestion that these shells are rotating; instead, we conclude that the observed kinematics is very probably caused by pulsations and random movements. The spatial distribution of the maser spots is found to be variable, but to show a stable axial symmetry.