  The MeerKAT International GigaHertz Tiered Extragalactic Exploration
(MIGHTEE) is one of the MeerKAT large survey projects, designed to pathfind SKA
key science. MIGHTEE is undertaking deep radio imaging of four well observed
fields (COSMOS, XMM-LSS, ELAIS S1 and CDFS) totaling 20 square degrees to
$\mu$Jy sensitivities. Broadband imaging observations between 880--1690 MHz
yield total intensity continuum, spectro-polarimetry, and atomic hydrogen
spectral imaging. Early science data from MIGHTEE are being released from
initial observations of COSMOS and XMM-LSS. This paper describes the
spectro-polarimetric observations, the polarization data processing of the
MIGHTEE early science fields, and presents polarization data images and
catalogues. The catalogues include radio spectral index, redshift information
and Faraday rotation measure synthesis results for 13,271 total intensity radio
sources down to a polarized intensity detection limit of $\sim$20
$\mu$Jy\,bm$^{-1}$. Polarized signals were detected from 324 sources. For the
polarized detections we include a catalogue of Faraday Depth from both Faraday
Synthesis and $Q$, $U$ fitting, as well as total intensity and polarization
spectral indices. The distribution of redshift of the total radio sources and
detected polarized sources are the same, with median redshifts of 0.86 and 0.82
respectively. Depolarization of the emission at longer-wavelengths is seen to
increase with decreasing total-intensity spectral index, implying that
depolarisation is intrinsic to the radio sources. No evidence is seen for a
redshift dependence of the variance of Faraday Depth.
