We present $^{12}$CO(2-1) line and 1300 $mu$m continuum observations made with the Submillimeter Array (SMA) of the young star DG Tau B. We find, in the continuum observations, emission arising from the circumstellar disk surrounding DG Tau B. The $^{12}$CO(2-1) line observations, on the other hand, revealed emission associated with the disk and the asymmetric outflow related with this source. Velocity asymmetries about the flow axis are found over the entire length of the flow. The amplitude of the velocity differences is of the order of 1 -- 2 km s$^{-1}$ over distances of about 300 -- 400 AU. We interpret them as a result of outflow rotation. The sense of the outflow and disk rotation is the same. Infalling gas from a rotating molecular core cannot explain the observed velocity gradient within the flow. Magneto-centrifugal disk winds or photoevaporated disk winds can produce the observed rotational speeds if they are ejected from a keplerian disk at radii of several tens of AU. Nevertheless, these slow winds ejected from large radii are not very massive, and cannot account for the observed linear momentum and angular momentum rates of the molecular flow. Thus, the observed flow is probably entrained material from the parent cloud. DG Tau B is a good laboratory to model in detail the entrainment process and see if it can account for the observed angular momentum.
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