  We report the detection of circular polarization in the compact radio jet of
the nearby spiral galaxy M81 (M81*). The observations were made with the Very
Large Array at 4.8 and 8.4 GHz and circular polarization was detected at both
frequencies. We estimate a value of $m_{c}=0.54\pm0.06\pm0.07%$ at 8.4 GHz and
$m_{c}=0.27\pm0.06\pm0.07%$ at 4.8 GHz for the fractional circular
polarization. The errors are separated into statistical and systematic terms.
The spectrum of the circular polarization is possibly inverted which would be
unusual for AGN. We also detected no linear polarization in M81* at a level of
0.1% implying that the source has a very high circular-to-linear polarization
ratio as found so far only in Sgr A*, the central radio source in our Galaxy.
This further supports the idea that M81* is a scaled-up version of Sgr A* and
suggests that the polarization properties are intrinsic to the two sources and
are not caused by a foreground screen in the Galaxy.
