Yes, it is entirely possible.
I'm sure you could if you could take a sketch to a tattoo artist. They could then tattoo it on your body (probably the left forearm, as that is where the Death Eaters have their Dark Marks). Unfortunately, it would not 'burn' or change colors. :-)
But why would any sane person want to? As Ron would say,"Are you mental?"
Try a Hungarian Horntail.