  This paper introduces a new Planck Catalog of Polarized and Variable Compact
Sources (PCCS-PV) comprising 153 sources, the majority of which are
extragalactic. The data include both the total flux density and linear
polarization measured by Planck with frequency coverage from 30 to 353 GHz, and
temporal spacing ranging from days to years. We classify most sources as
beamed, extragalactic radio sources; the catalog also includes several radio
galaxies, Seyfert galaxies, and Galactic and Magellanic Cloud sources,
including H IIi regions and planetary nebulae. An advanced extraction method
applied directly to the multifrequency Planck time-ordered data, rather than
the mission sky maps, was developed to allow an assessment of the variability
of polarized sources. Our analysis of the time-ordered data from the Planck
mission, tod2flux, allowed us to catalog the time-varying emission and
polarization properties for these sources at the full range of polarized
frequencies employed by Planck, 30 to 353 GHz. PCCS-PV provides the time- and
frequency-dependent, polarized flux densities for all 153 sources. To
illustrate some potential applications of the PCCS- PV, we conducted
preliminary comparisons of our measurements of selected sources with published
data from other astronomical instruments. In summary, we find general agreement
between the Planck and the Institut de Radioastronomie Millim\'etrique (IRAM)
polarization measurements as well as with the Mets\"ahovi 37 GHz values at
closely similar epochs. These combined measurements also show the value of
PCCS-PV results and the PCCS2 catalog for filling in missing spectral (or
temporal) coverage and helping to define the spectral energy distributions of
extragalactic sources. In turn, these results provide useful clues as to the
physical properties of the sources.
