Are armorers allowed to issue themselves a weapon or does the alternate armorer have to issue the primary armorers' weapon?

The question seems to be about the paperwork but everyone except SGM Bill Frazer is answering about the armorer having a weapon -- which completely misses the point.

Since (Join to see)'s profile shows him as a civilian with no military connection, I can't begin to guess the real basis for asking this (and honestly I am not convinced the profile is genuine).

It has been many years since I worked as an armorer, and I know that procedures have absolutely changed since then, but I think I see the point. The armorer is responsible for all the UNISSUED weapons in the arms room. When the armorer signs a weapon out to someone, that individual becomes responsible for the weapon and the weapon is no longer "in the arms room." The paperwork used to keep track of the responsibility for weapons and other sensitive items is created on the basis of responsibility being transferred from one person to another. Personally I don't see an overwhelming problem with an armorer issuing a weapon to himself, but I can easily see how some Bean Counter might have a problem with it.

If the armorer is already responsible for all the weapons in the arms room, does he even need to sign for the one that he takes from the rack and puts in his holster while he and the weapon are both staying in the arms room?? If the armorer signs the weapon out to himself, who is checking that it is the correct weapon? Supposedly when the armorer issues a weapon, both parties check the serial number, and both parties check it again when the weapon is returned.

We don't know which service (Join to see) is asking about, but each service has its own regulations covering accountability for weapons and sensitive items. The applicable regulation would be the starting point (for the Army AR 190-11, if I recall correctly). Installations may have additional regulations and units will have policies to implement those regulations.