It is quite normal for that happen because when you read, you may just have one eye dominant, so that the other one being weaker. It can also be said like that the eye muscles in one of your eyes is too weak, so when you read, your eyes tend to fight one another after a while. You can go to your optometrist to have a check. Good luck!
When you find such situation, you'd better check whether your eyes have the problems. You may get infection at the eyes because of the coming bacterium. That is the main reason of your cross eyes when reading. You could use the eye drops to get rid of the bacterium and make the eyes feel comfortable. You could have a try.
It's quite possible that your eyes get crossed. When you are reading, your two eyes will both focus on the small words, your eyes are not in relaxed status, with tension eye muscles, you easily find your eye cross when you are reading. Therefore, to correct your crossed eyes, you can relax your eyes for a while, and do some eye exercises to relieve it. But if your eye cross is permanent, you can consult a doctor or receive surgeries to correct it.