I think that the only thing available to work with is the shape argument:
library(ggplot2)
p <- ggplot(mtcars, aes(wt, mpg))
par(mfrow=c(2,2))
p + geom_point(shape = 5) + coord_polar()

p + geom_point(shape = "k", size = 3) + coord_polar()

p + geom_point(shape = ".") + coord_polar()

p + geom_point(shape = NA) + coord_polar()
#> Warning: Removed 32 rows containing missing values (geom_point).

Created on 2020-04-02 by the reprex package (v0.3.0)