  The Crab nebula is a supernova remnant exhibiting a highly polarized
synchrotron radiation at radio and millimeter wavelengths. It is the brightest
source in the microwave sky with an extension of 7 by 5 arcminutes and commonly
used as a standard candle for any experiment which aims at measuring the
polarization of the sky. Though its spectral energy distribution has been well
characterized in total intensity, polarization data are still lacking at
millimetre wavelengths. We report in this paper high resolution (18 arcsec
FWHM) observations of the Crab nebula in total intensity and linear
polarization at 150 GHz with the NIKA camera. NIKA, operated at the IRAM 30 m
telescope from 2012 to 2015, is a camera made of Lumped Element Kinetic
Inductance Detectors (LEKIDs) observing the sky at 150 and 260 GHz. From these
observations we are able to reconstruct the spatial distribution of the
polarization degree and angle of the Crab nebula, which is found to be
compatible with previous observations at lower and higher frequencies.
Averaging across the source and using other existing data sets we find that the
Crab nebula polarization angle is consistent with being constant over a wide
range of frequencies with a value of -87.7$^\circ$ +- 0.3 in Galactic
coordinates. We also present the first estimation of the Crab nebula spectral
energy distribution polarized flux in a wide frequency range: 30-353 GHz.
Assuming a single power law emission model we find that the polarization
spectral index $\beta_{pol}$ = - 0.347 +- 0.026 is compatible with the
intensity spectral index $\beta$ = - 0.323 +- 0.001.
