You should probably check on the definition of rape because just because someone is your girlfriend does not mean they are yours for you to have sex with whenever you want or against their will. You still need consent. I don't believe this scenario to be a case of rape but people have been charged for drunken sex even though it was almost certainly consensual at the time (but there are also cases where someone is too drunk to properly consent so it can often be a tricky area legally).