  We present results of long-term multi-wavelength polarization observations of
the powerful blazar 3C~279 after its $\gamma$-ray flare on 2013~December 20. We
followed up this flare with single-dish polarization observations using two
21-m telescopes of the Korean VLBI Network. Observations carried out weekly
from 2013~December~25 to 2015~January~11, at 22~GHz, 43~GHz, 86~GHz
simultaneously, as part of the Monitoring Of GAmma-ray Bright AGN (MOGABA)
program. We measured 3C~279 total flux densities of 22--34~Jy at 22~GHz,
15--28~Jy (43~GHz), and 10--21~Jy (86~GHz), showing mild variability of $\leq
50\,\%$ over the period of our observations. The spectral index between 22~GHz
and 86~GHz ranged from $-0.13$ to $-0.36$. Linear polarization angles were
27$^{\circ}$--38$^{\circ}$, 30$^{\circ}$--42$^{\circ}$, and
33$^{\circ}$--50$^{\circ}$ at 22~GHz, 43~GHz, and 86~GHz, respectively. The
degree of linear polarization was in the range of 6--12\,\%, and slightly
decreased with time at all frequencies. We investigated Faraday rotation and
depolarization of the polarized emission at 22--86~GHz, and found Faraday
rotation measures (RM) of $-300$ to $-1200$~rad~m$^{-2}$ between 22~GHz and
43~GHz, and $-800$ to $-5100$~rad~m$^{-2}$ between 43~GHz and 86~GHz. The RM
values follow a power law with a mean power law index $a$ of $2.2$, implying
that the polarized emission at these frequencies travels through a Faraday
screen in or near the jet. We conclude that the regions emitting polarized
radio emission may be different from the region responsible for the 2013
December $\gamma$-ray flare and are maintained by the dominant magnetic field
perpendicular to the direction of the radio jet at milliarcsecond scales.
