Broke ball joint, Then this

I broke a ball joint on my 1g tsi. After i fixed the ball joint, now i hear this scraping noise from my front left wheel. I took off the wheel and saw that my rotor is scraped up around the outside of the rotor (rotor was just replaced about a month ago). My wheel moves side to side about 1/2 an inch, is that normal??
Does anyone know what could be wrong????

What do you mean side to side. Like say you sit down facing the wheel, can you push/pull the wheel in/out of the hub, or if you grab the front and back of the tire and wiggle it side to side. The scraping could be the rotor guard scraping up against the rotor, and/or you may have a loose hub or a bad wheel bearing.

If you beat the piss out of the rotor when changing it a month ago, you may have taken out the wheel bearing with it.

I 2nd the wheel bearing. Sounds like your problem. I've never replaced one in a DSM, but I'm guessing its a PITA.

It moves when I sit down facing the wheel, and I can push/pull the wheel about 1/2 of an in.

Bearing is bad. You have to buy the bearing, inner and outer seals. Take off the hub assembly and bring it to a machine shop and get it pressed out and new one pressed in. Make sure they pack it with grease. I would count on the otherside going bad soon. Don't ride on it too long or you may wear the hub out of spec and render it useless for a new bearing.

also when i steer to the right it makes the scraping noise. When i steer to the left it makes the noise but very softly only.

Don't drive it until you fix it. The longer you go without repairing it, the more you will ruin.

also when i steer to the right it makes the scraping noise. When i steer to the left it makes the noise but very softly only.

That means the left side is bad.