Can I get approved for an auto loan?

I want to buy a car that is $26,000 out the door I am hoping to talk them down to 24-25k. I would like to finance it for 72 months and put $8,000 down. I have a low limit credit card that I've had for two years and I am only 20. I work full time and my gross monthly income is $3,100. My credit score is 626 but I've been turned down on credit cards so would I be able to finance a loan by myself or do I need a co-signer? Also this is my first time buying a car and I do not have any other debt.