Yes your brother should be able to sign for your FedEx package.
In fact anyone in your household as long as they're 18 or older can sign for the FedEx package to be dropped off.
If no one is home to sign for the FedEx package then they should leave a hangar on your door where you can sign it which would allow FedEx to leave the package at your door.
Or you can also have a FedEx package held for pickup at a FedEx location.