While in the United States, you may periodically be issued one for training purposes, which you will turn in at the end of the training event. This will usually be a Beretta M9 pistol (9mm), but sometimes a M4 or M16 rifle. Weapons aren't issued to you during your normal periods of work as a physician.
You are, of course, able to buy your own gun(s), subject to the laws of the state you're stationed in. There are rules governing their storage and transport if you live on base. If you live off base, you will never bring your personally owned firearms on base, unless it's specifically to and from a range open for non-official use. You will never be authorized to use a personally owned firearm for military training events or deployments.
While deployed to a dangerous area, you will be issued a M9. It's not unheard of for medical personnel to be issued rifles, but it's somewhat unusual, given the whole medical personnel / Geneva convention / "defensive" weapons thing.