We have carried out a kinematical , high angular resolution ( \sim 0 \farcs 1 ) study of the optical blueshifted flow from DG Tau within 0 \farcs 5 from the source ( i.e . 110 AU when de-projected along this flow ) . We analysed optical emission line profiles extracted from a set of seven long-slit spectra taken with the Space Telescope Imaging Spectrograph ( STIS ) on board the Hubble Space Telescope ( HST ) , obtained by maintaining the slit parallel to the outflow axis while at the same time moving it transversely in steps of 0 \farcs 07 . For the spatially resolved flow of moderate velocity ( peaking at -70 km s ^ { -1 } ) , we have found systematic differences in the radial velocities of lines from opposing slit positions i.e . on alternate sides of the jet axis . The results , obtained using two independent techniques , are corrected for the spurious wavelength shift due to the uneven illumination of the STIS slit . Other instrumental effects are shown to be either absent or unimportant . The derived relative Doppler shifts range from 5 to 20 km s ^ { -1 } . Assuming the flow is axially symmetric , the velocity shifts are consistent with the southeastern side of the flow moving towards the observer faster than the corresponding northwestern side . If this finding is interpreted as rotation , the flow is then rotating clockwise looking from the jet towards the source and the derived toroidal velocities are in the range 6 to 15 km s ^ { -1 } , depending on position . Combining these values with recent estimates of the mass loss rate , one would obtain an angular momentum flux , for the low to moderate velocity regime of the flow , of \dot { J } _ { w,lm } \sim 3.8 10 ^ { -5 } M _ { \odot } yr ^ { -1 } AU km s ^ { -1 } . Our findings may constitute the first detection of rotation in the initial channel of a jet flow . The derived values appear to be consistent with the predictions of popular magneto-centrifugal jet-launching models , although we can not exclude the possibility that the observed velocity differences are due to some transverse outflow asymmetry other than rotation .