“Clerics shall entirely abstain from all those things that are indecent to their state; they shall not engage in indecorous arts; they shall abstain from gambling games with risks of money; they shall not carry arms, except when there is just cause for fearing; hunting should not be indulged, and [then] never with clamor; taverns and similar places should not be entered without necessity or another just cause approved by the local Ordinary.” - Canon 138, 1917 Code
Every person has the natural-law right to self-defense, regardless of their state in life.
I am assuming by "not carry[ing] arms", this refers to open- or concealed-carry in the course of everyday life when there is no foreseen need for self-defense. It seems that a priest would be able to engage in shooting practice, as at a gun range, simply as a hobby. The only thing I've ever shot, aside from a target, was a severely wounded bird in my backyard, to put it out of its misery, and that was with a high-powered .22 air rifle. (BTW, I am a layman.) I think our HOA would frown on firearms.