We present new CRIRES spectroscopic observations of the Br{gamma} emission line in the nuclear region of the Circinus galaxy, obtained with the aim of measuring the black hole (BH) mass with the spectroastrometric technique. The Circinus galaxy is an ideal benchmark for the spectroastrometric technique given its proximity and secure BH measurement obtained with the observation of its nuclear H_2_O maser disk. The kinematical data have been analyzed both with the classical method based on the analysis of the rotation curves and with the new method developed by us that is based on spectroastrometry. The classical method indicates that the gas disk rotates in a gravitational potential resulting from an extended stellar mass distribution and a spatially unresolved dynamical mass of (1.7+/-0.2)x10^7^M_{sun}_, concentrated within r<7pc, corresponding to the seeing-limited resolution of the observations. The new method is capable of probing the gas rotation at scales that are a factor ~3.5 smaller than those probed by the rotation curve analysis, highlighting the potential of spectroastrometry. The dynamical mass, which is spatially unresolved with the spectroastrometric method, is a factor ~2 smaller, 7.9^+1.4^_-1.1_x10^6^M_{sun}_, indicating that spectroastrometry has been able to spatially resolve the nuclear mass distribution down to 2 pc scales. This unresolved mass is still a factor ~4.5 larger than the BH mass measurement obtained with the H_2_O maser emission, indicating that even with spectroastrometry, it has not been possible to resolve the sphere of influence of the BH. Based on literature data, this spatially unresolved dynamical mass distribution is likely dominated by warm molecular gas and has been tentatively identified with the circum-nuclear torus that prevents a direct view of the central BH in Circinus. This mass distribution, with a size of ~2pc, is similar in shape to that of the star cluster of the Milky Way, suggesting that a molecular torus, forming stars at a high rate, might be the earlier evolutionary stage of the nuclear star clusters that are common in late-type spirals.