  We test the relationship between UV-derived star formation rates (SFRs) and
the 7.7 ${\mu}$m polycyclic aromatic hydrocarbon (PAH) luminosities from the
integrated emission of galaxies at z ~ 0 - 2. We utilize multi-band photometry
covering 0.2 - 160 ${\mu}$m from HST, CFHT, JWST, Spitzer, and Herschel for
galaxies in the Cosmic Evolution Early Release Science (CEERS) Survey. We
perform spectral energy distribution (SED) modeling of these data to measure
dust-corrected far-UV (FUV) luminosities, $L_{FUV}$, and UV-derived SFRs. We
then fit SED models to the JWST/MIRI 7.7 - 21 ${\mu}$m CEERS data to derive
rest-frame 7.7 ${\mu}$m luminosities, $L_{770}$, using the average flux density
in the rest-frame MIRI F770W bandpass. We observe a correlation between
$L_{770}$ and $L_{FUV}$, where log $L_{770}$ is proportional to (1.27+/-0.04)
log $L_{FUV}$. $L_{770}$ diverges from this relation for galaxies at lower
metallicities, lower dust obscuration, and for galaxies dominated by evolved
stellar populations. We derive a "single-wavelength" SFR calibration for
$L_{770}$ which has a scatter from model estimated SFRs
(${{\sigma}_{{\Delta}SFR}}$) of 0.24 dex. We derive a "multi-wavelength"
calibration for the linear combination of the observed FUV luminosity
(uncorrected for dust) and the rest-frame 7.7 ${\mu}$m luminosity, which has a
scatter of ${{\sigma}_{{\Delta}SFR}}$ = 0.21 dex. The relatively small decrease
in ${\sigma}$ suggests this is near the systematic accuracy of the total SFRs
using either calibration. These results demonstrate that the rest-frame 7.7
${\mu}$m emission constrained by JWST/MIRI is a tracer of the SFR for distant
galaxies to this accuracy, provided the galaxies are dominated by
star-formation with moderate-to-high levels of attenuation and metallicity.
