Yes you can i am on the pill and i get my period every month for about 4 days.
Most birth controls have "active" pills which contain the actual hormones that prevent pregnancy, they are a different color from the "sugar" pills which dont have any hormones in them at all. You start with the active pills and they last through your cycle, then when you have taken the last active pill you begin taking the sugar pills which there are usually about 7 of them. During the time that you are taking those sugar pills it is normal to get your period, that is actually what is supposed to happen anyway. Now if you were to get your period during the active pills, then you need to think if maybe you missed a pill somewhere. Some birth controls can make you have some bleeding if you miss one or more. This is no cause of alarm, just a nice little reminder to no miss them, or that is what will happen. If you are concerned, then dont hesistate to give you local family planning clinic or your health care provider whom prescribed you the pills and ask them any questions you may have. They will be happy to give you any information you need.