  The magnetar 4U~0142+61 has been well studied at optical and infrared
wavelengths and is known to have a complicated broad-band spectrum over the
wavelength range. Here we report the result from our linear imaging polarimetry
of the magnetar at optical $I$-band. From the polarimetric observation carried
out with the 8.2-m Subaru telescope, we determine the degree of linear
polarization $P=1.0\pm$3.4\%, or $P\leq$5.6\% (90\% confidence level).
Considering models suggested for optical emission from magnetars, we discuss
the implications of our result. The upper limit measurement indicates that
different from radio pulsars, magnetars probably would not have strongly
polarized optical emission if the emission arises from their magnetosphere as
suggested.
