I am not a doctor, but I took flight physiology in college and I've had a scrotum longer than I've been breathing air so here is my understanding:

Technically no, the scrotum can't cramp because it doesn't have skeletal muscles. It can constrict like most skin, you get goosebumps on your arm, your balls are either pulled up secure or let loose and dangling, but it can't overdo that the way, say, your calf muscle can.

But, there's a lot of kinds of pain that can occur in the lower abdomen/upper leg that can feel like it's coming from the scrotum or testicles. Groin muscles (the ones that pull the legs together) can cramp, several abdominal or urinary issues can present as a cramping sensation in the groin, as Hugh Grant said on Top Gear, some back issues can present as "bollock pain," and issues with the testicles or their associated plumbing can present with cramp-like pain.

Any sudden or severe pain in the testes is reason to talk to a doctor and "it feels like a cramp in my scrotum" may be useful troubleshooting information to provide during that conversation.