For some people spotting is normal and so is cramping. How much are you spotting? What color is it? Usually if it is light pink or brown it is normal. It is concerning if it is bright red as that means new blood esp if you start to pass any clots. The cramping is normal esp if it is just light cramping. The light cramping is just from your uterus getting ready for the pregnancy and stretching in there. If the cramping is severe then it's time to get things looked at more. Either way, normal or not normal, I would call your doctors office and let them know what is going on. They may want to see you or get some blood work to check your HCG levels. Hope everything turns out ok. For now call your doctor, drink plenty of water, and put your feet up.
The short answer is yes it can be normal. Is it normal for you? That's hard to say. Since you are spotting AND cramping it would be highly adviseable for you to contact your doctor asap.