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=1.0pm$3.4%, or $Pleq$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.
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