Jill Biden's Secret Service agent might be the butt of a few jokes around the office after shooting himself ... because he reportedly popped a cap in his own ass!

A new report from Susan Crabtree -- a veteran journalist with RealClearPolitics -- claims the agent who injured himself while on duty at Philadelphia International Airport shot himself in the buttocks, not the leg, like initial reports indicated.

Crabtree says the accidental shooting occurred when the agent rushed back to the SUV the detail traveled in to get his cell phone ... and used the flashlight on his service weapon to try to find it. He blasted his bottom while holstering the weapon, according to Crabtree.

A senior Secret Service official tells TMZ … the agent did shoot himself while attempting to reholster his gun, but it's unclear why he took the gun out in the first place. As for the shot in the ass ... our source couldn't confirm it because the part about the agent using his gun as a flashlight was not reported to the department.

However, this official did say it's "accurate that the agent suffered an unintentional, self-inflicted gunshot wound to his hip area. He was treated at an area hospital."

The matter is under investigation by the Secret Service's Office of Professional Responsibility ... and the agency cannot publicly comment about additional specifics during the investigation. The Secret Service has confirmed the agent did not shoot himself in the leg as was first reported.

Resist the urge to laugh ... as Forrest Gump will attest, getting shot in the butt is no joke!F