If you have the coordinates of the points you want to plot in two columns of a matrix, you can simply use the plot function on that matrix. You don't need to use ggplot here. But of course, you can use it.
See below:
r <- 1
theta <- seq(from = -pi,
to = pi,
length.out = 1e+3)
u <- (r * cos(x = theta))
v <- (r * sin(x = theta))
data_in_matrix <- cbind(u, v)
# base plot function
plot(data_in_matrix,
asp = 1)
# using ggplot2
library(ggplot2)

# quickplot
quickplot(x = u,
y = v,
data = as.data.frame(x = data_in_matrix))

# ggplot
ggplot(data = as.data.frame(x = data_in_matrix),
mapping = aes(x = u,
y = v)) +
geom_point()

Created on 2019-04-07 by the reprex package (v0.2.1)