I'm trying to make a similar shape to this stamp without using "Image Trace"
I tried drawing a basic pattern to wrap it around a circle but I didn't know how to do it. Or is there an easier way to make the above shape?
You can make it with the star tool. I count 12 points, so enter that and then 10 units for first radius and 9 units for 2nd radius. I used inches and it converted them to points. The important ratio is 9-10 for this kind of star.
Round the corners. Your star may be a different size so need a differing amount of roundness to achieve the look.