It’s been month since I stopped working but I haven’t received my 1 week check. How can get it?

In GA, employers are not required to provide employees with vacation benefits.  However, to the extent that an employer chooses to do so, it must comply with the terms of established policy or any applicable employment/union contract. Also, an employer may establish a policy or enter into a contract that denies employees payment for accrued vacation leave upon voluntary/involuntary separation from employment. Additionally an employer may establish a policy or enter into a contract disqualifying employees from payment of accrued vacation upon separation from employment if they are terminated or if they fail to comply with specific requirements (e.g. giving a 2 week notice). 
That all having been said, if there is no policy or contract as to whether or not an employee must be paid for accrued vacation upon separation from employment, it is unlikely an employer would be obligated to pay an employee for such time unless the employer has a practice of doing it. 
At this point, you can file a complaint with your state's department of labor and/or sue your former employer in small claims court. You can also consult directly with a local employment law attorney.