This was added here
It should be sf from 0.6.4 (see news: Changelog • sf)
sf should work from R 3.3 so not sure it is that. System requirements are
GDAL (>= 2.0.1), GEOS (>= 3.4.0), PROJ (>= 4.8.0)
Can you get the log for your API from the log pane inside RStudio Connect ?
You should have a R error somewhere in that log.