Is it common to have periods during early pregnancy?

No: By definition you cannot have a period when you are pregnant. You can experience vaginal bleeding during pregnancy and this is not normal. Bleeding during pregnancy should be promptly evaluated by your doctor.

See below: It is not exactly common, but it is not unheard of, either. It does happen enough that it is a known variant of normal pregnancy.

Light spotting may: Occur during implantation of the fertilized egg due to irritation of the endometrial lining with small rupture of blood vessels