FIG. 1 is a front perspective view of the new ornamental curling iron of the present invention. FIG. 2 is a left side view thereof. FIG. 3 is a right side view thereof. FIG. 4 is a rear perspective view thereof. FIG. 5 is a front view thereof. FIG. 6 is a rear view thereof. FIG. 7 is a bottom view thereof; and, FIG. 8 is a top view thereof.