Spreaking of grammar, you should conjugate the verb 'wake' in it's past participle tense every time it comes with 'have' or any variation of it. So the correct thing to say would be:

"I wish I had woken up early/earlier" - But as you are flexing the verb to the past form, you are referring to the past, and this expresses a regret. Something you didn't do but you wish you had done.

"I wish I could wake up early" - Could expresses the idea of possibility or ability. You can't do it now, it's hard for you. In this case, you are talking about a habit. Something you wish you could do differently.

I wish I wake up doesn't sound ok for me, I'm not sure if tou can use it, I think that, grammatically speaking, the appropriate form of this sentence would be: "I wish I woke up early" - Which in this case expresses simply a wish, similar to "I wish I could..."

I hope this was helpful! :D