Numbers differ by study and vaccine. The prescribing info for phizer mentions bells palsy, but not the calculated rate.

An analysis looking at the trial data puts it at 14-18/100k higher than the expected baseline

https://www.thelancet.com/journals/laninf/article/PIIS1473-3...

A analsys from the previously linked lancet study had a muck larger sample ~500k, but different collection methods and found smaller but nonzero results

>The age-standardised difference for the incidence compared with the background population was 41·5 (95% CI 11·7 to 71·4) for CoronaVac and 17·0 (−6·6 to 40·6) for BNT162b2, equivalent to an additional 4·8 cases per 100 000 people vaccinated for CoronaVac and 2·0 cases per 100 000 people vaccinated for BNT162b2.

Most if not all the vaccine trials saw small increases <1% in serious adverse events in the treatment arm