Can you work for border patrol if you're convicted felon for going AWOL from the military and charged with desertion?

No. I'd be surprised if ANY Federal Agency would hire you, particularly an Agency which requires any level of security clearance.

Hello P:

No. You can't carry a gun, and cops do that - even border ones.

excon

No you can not work for any agency with police powers. Second even if you could, the border patorl gets about 300 applications for any one job filled, so you would need normally a perfect record, a college degree and either military or other police background