Is it normal to experience cramping on alesse? I've been taking it for the last 3 weeks and I've been having period like cramping randomly.

It can. If you just started it that can be normal and will go away. You can take Ibuprofen for the pain. It should go away. If it doesn't then talk with your health provider.
May be ovualtion. Alesse is one of the "very low dose" birth control pills (bcp). For some women, that dose of estrogen is not adequate to completely suppress ovulation. If you ovulate you can have cramps - you also could conceive, and that risk is 2 or 3 times higher with the very low dose bcp's - like alesse. The risk of spotting is also higher with Alesse for the same reason.