There's nothing wrong with having a relationship, as long as you don't become absorbed by it.
You just have to decide, did you make this decision to not get in a relationship because you thought that and game were mutually exclusive at the time? Or are you now just being wrapped up in the emotions around this girl, and are just having some strong chemical reactions?
Sit down and think about this girl objectively. Who is she, rather than how does she make you feel. What kind of job does she have? Does she have an education? What traits does she have that you want? That you don't want? It's usually best to come up with a list like this before meeting any specific girl, because otherwise, the list will sometimes subconsciously mimic the girl, because you want her...
But too late now, so don't worry about it. Just try to look a her objectively.One last thing to think about is how are you going to feel about yourself, knowing that you're breaking a promise to yourself? That may have negative effects on your psche. I've studied some psychology, and know that doing something like this is subtly sending yourself messages, that will be the opposite of positive affirmations.
Regardless! All the above being said, I'm not trying to dissuade you from getting with this girl. It may be one of the best things you ever do, either positively, or if turns out bad, an awesome learning experience. All I want to do here is just make you aware of things, so that your mind can sort through your decision, rather than just being blinded by chemicals running through your brain.
As for how to do it, I'd recommend just starting by taking hr out on a lot of dates. I'm not saying often. Don't take her on five dates a week or something, but one or two dates a week for a month or two. Make sure you like what you see. Then yu can work on building a relationship.