Is it possible to fracture your penis?

Yes. A penis fracture can occur when there is trauma to the erect penis.

During an erection, the penis is engorged with blood. If the penis is bent suddenly or forcefully while it's engorged, the trauma may rupture the lining of one of the two cylinders in the penis (corpus cavernosum) responsible for erections — resulting in a penis fracture. The trauma is usually related to aggressive or acrobatic sexual intercourse or, in some cases, aggressive masturbation.

A penis fracture is a painful injury that's often accompanied by an audible cracking sound, followed immediately by dark bruising of the penis due to blood escaping the cylinder. In some cases the tube that drains urine from the body (urethra) may be damaged as well, and blood may be visible at the urinary opening of the penis.

A penis fracture requires urgent medical attention. A penis fracture can usually be diagnosed with a physical exam, and prompt surgical repair is typically recommended. Left untreated, a penis fracture may result in deformity of the penis or the inability to have or maintain an erection (erectile dysfunction).

References:

https://en.wikipedia.org/wiki/Penile_fracture

http://www.menshealth.com/health/what-is-a-penile-fracture