How can I create rectangles in ggplot with known centers, dimensions and orientations

There is no convenient way of doing this. You'd have to reparametrise the rectangles as polygons and perform the affine transformation yourself.

library(tidyverse)

tbl <- tibble(center_x = c(10, 50),
              center_y = c(20, 30),
              width = c(4, 7),
              length = c(8, 12),
              angle = c(120, 45), # degrees
              color = c("blue", "yellow"))

poly <- tbl %>%
  mutate(
    id = seq_along(center_x),
    xmin = - 0.5 * width,
    xmax = + 0.5 * width,
    ymax = + 0.5 * length,
    ymin = - 0.5 * length,
    rads = angle / 180 * pi
  ) %>%
  pivot_longer(c("xmax", "xmin"), "xpos", values_to = "x") %>%
  pivot_longer(c("ymax", "ymin"), "ypos", values_to = "y") %>%
  group_by(id) %>%
  mutate(
    y = y[c(1, 2, 4, 3)], # prevent hourglass polygons
    xrot = x * cos(rads) - y * sin(rads),
    yrot = y * cos(rads) + x * sin(rads)
  )

ggplot(poly) +
  geom_polygon(
    aes(x = center_x + xrot,
        y = center_y + yrot,
        group = id, fill = I(color))
  ) +
  coord_equal()

^{Created on 2021-11-16 by the reprex package (v1.0.0)}