As far as I know—and I’m no expert in 5e but fiend’s answer confirms—there is not currently any official option in 5e for this.
But there was in 3.5e: the Lords of Madness sourcebook included the mouthpick magic weapon property that allowed creatures with a bite attack to wield the mouthpick weapon instead of biting. It didn’t grant proficiency with the weapon, which meant that for an animal companion, you almost certainly wanted the animal companion to take the Martial Weapon Proficiency for the weapon, but the rules allowed an animal companion to do that.
Already, I think, it’s clear that 3.5e was rather different from 5e in some regards, and one of those was that both feats and magic items were rather more common (but also somewhat less individually potent). For example, pretty much all characters1 started with at least one feat, and got a feat every three levels. That included animal companions. And characters could use as many magic items as they had room for, and magic weapons went as high as +10, rather than +3. That changes the relative value of a feat and a magic weapon.
In 5e, animal companions don’t get feats. There isn’t any rule available that could grant weapon proficiency to an animal companion. And a mouthpick weapon counting as a +2 weapon simply doesn’t mean the same thing when that is 2/10 instead of 2/3.
The feat thing would have been easy enough to handle in 3.5e, though: aptitude weapons can be used proficiently by anyone. As aptitude was, like mouthpick, a +1-equivalent property, a +1 mouthpick aptitude weapon was a +3-equivalent—3/10, that is.
So it seems to me that a +1 magic weapon in 5e could be roughly equivalent to a +3-equivalent weapon in 3.5e. Therefore, I think a magic weapon with a +1 bonus that can be wielded proficiently by any creature with a bite attack (replacing that bite attack) is probably a fair port of the 3.5e material. So something like this:
Weapon (any melee weapon), rare (requires attunement)
You gain a +1 bonus to attack and damage rolls made with this magic weapon.
You can only wield this weapon if you have a bite attack. While wielding this weapon, you cannot use your bite attack, but you are proficient with attacks with this weapon.
But I must caution that I am not an expert in 5e, and I certainly have not actually tried this in 5e.
There are some weapons that are magical, but do not have a + 1 to hit (flame tongue, dancing sword, frost brand, mace of disruption) so this same approach can be made without adding + to hit if your DM raises an eyebrow at this mouthpick proposal. Dropping the +1 should reduce the rarity to uncommon, from rare, which is a better fit at 3rd level than a rare item.
As with any homebrew proposal, sit down with your DM and discuss this in detail to make sure it fits in with your campaign and his setting.
- Excepting only mindless, Int –, creatures like skeletons and swarms of insects.