The function does not appear to draw the height axis for some reason. I have neither seen much examples of it online - all circular dendrograms appear to omit it. So, I embarked on a task to add it myself.

The following code appears to do it:

mat <- matrix(abs(rnorm(100)),10,10)
dimnames(mat) <- list(letters[1:10],letters[1:10])
ma2 <- as.dist(mat)
hc <- hclust(ma2)
dend <- as.dendrogram(hc)

par(mfrow=c(1,2))

plot(dend)

require(circlize)
require(dendextend)

#Get the heights for each branch
heights <- round(get_branches_heights(dend, sort=FALSE), 1)

#Get max height
maxHeight= max(heights)

#Set label and dendrogram height for circular dendrogram
labelHeight=0.1
dendHeight=0.8

#Draw the circular dendrogram
circlize_dendrogram(dend,
  facing = "outside",
  labels = TRUE,
  labels_track_height = labelHeight,
  dend_track_height = dendHeight)

# Create tick co-ordinates and values for the new axis
# We have to ensure that we don't overlap the label plot region
#   (height specified by labelHeight), nor the central region of the
#   plot (1-(dendHeight+labelHeight))
ticks <- seq(from = (1-(dendHeight+labelHeight)),
  to = (1-labelHeight), length.out=5)
values <- round(rev(seq(from=0, to=maxHeight, length.out=5)), 1)

#Add the new axis
require(plotrix)
ablineclip(h=0, v=ticks, col="black",
  x1=1-(dendHeight+labelHeight),
  x2=1-labelHeight,
  y1=0,
  y2=0.04,
  lwd=1.5)
text(ticks, 0+0.08, values, cex=0.8)
text(
  (1-labelHeight)-(((1-labelHeight)-(1-(dendHeight+labelHeight)))/2),
  0+0.14,
  "Height", cex=0.8)