Your score is probably fine, however…
Home owners do run credit check, but your credit score is less interesting than your actual credit report.
It’s common for young people to have lower scores on average. Usually, it’s because of no credit (lack of credit history) rather than bad credit. You renters will want to see if you have negative items on your report such as late payments, charge-offs etc. If you tend not to pay debts, then they will not want to let you the apartment.
If it’s just a case of “thin” file, then usually the credit check won’t pose a problem.
Apartments have various other requirements. You may have to show sufficient wages to pay the rent. It goes without saying that all of your friends will have to qualify as well.
If you can’t meet their requirements, you may need to come up with a co-signer that will be liable to pay the rent in case that you fail to.
Please see also credit-score-and-renting.html for more information.