I'm not sure this is possible with circular, but it can be done in ggplot with a bit of data manipulation. Although you did not include it in your question, I assume ACT34_radarplot_input is just a vector of numbers between 0 and 24, so we can replicate it like this:
set.seed(1)
ACT34_radarplot_input <- runif(300, 0, 24)
You can reshape and plot this in gpplot as follows:
library(tidyverse)
ACT34_radarplot_input %>%
hist(breaks = seq(0, 24, 0.2), plot = FALSE) %>%
`[`(c(2, 4)) %>%
as_tibble() %>%
group_by(mids) %>%
summarize(y = -seq(counts), .groups = "drop") %>%
filter(y < 0) %>%
ggplot(aes(mids, y)) +
geom_point(col = "red2", size = 3) +
geom_hline(yintercept = 0) +
scale_x_continuous(breaks = c(0:24), limits = c(0, 24)) +
ylim(c(-20, 0)) +
coord_polar() +
ggtitle("Act 34 Significant Genes Phases") +
theme_void() +
theme(axis.text.x = element_text(size = 16),
plot.title = element_text(size = 20, hjust = 0.5))

dput(ACT34_radarplot_input)?