Is it abnormal to have a period with blood clots?

Generally, yes: Presence of clots generally indicates heavy bleeding that may lead to anemia. Even if the bleeding is not painful you may wish to consult a doctor. In the mean time, you should take iron supplements to keep from getting low in hemoglobin.

May be: If there is excessive bleeding, clotting of blood is normal, why there is excessive bleeding is to be determined by your gynecologist.