I woke up in the morning and I'm feeling a rapid heartbeat. Is this normal?

Not always. There could be a ton of causes. Talk to your doctor. You might be best served to ask for an event monitor or a constant heart monitor for a few days to see if you are having true cardiac palpitations or arrhythmias.
Count it. Try to count the rate. If you can report the heart rate, we can get a better idea if it's a normal rhythm or not. Do you wake up with free floating anxiety (as many people do?)- if yes, that's a typical cause of early morning rapid heart rate and it's not a disease, it's normal physiology.