Yes, having your period can drop your milk supply, but you can take calcium/magnesium supplements to regulate it.
The drop in milk supply that is associated with your period can be associated with a drop in blood calcium levels which occurs in the middle of your menstrual cycle, around the time that you ovulate. To combat this, you can take a calcium/magnesium supplement.
You can also try an herbal breastfeeding tea, or another galactagogue to help boost your milk supply. Talk to your doctor, a lactation consultant or a local breastfeeding group for advice and assistance.