While not a contender for the worst video game weapon full stop, I think the "Kozlice" over/under shotgun in Operation Flashpoint deserves a mention. It's easily the worst weapon in the game. You can only load two rounds at a time - a slug in one barrel, and a shell in the other. The shell is halfway decent, but the slug isn't powerful enough so it frequently takes more than one shot to down a single foe. Either way, you're lucky to get one kill per shot, and with only two shots per 3 second reload, that's a pitifully low rate of fire. To make things worse, each slug/shell takes up one primary inventory slot (there are 10), while a 30 round magazine for any assault rifle would fit in the same slot. This means that, using a Kozlice, you can carry a maximum of 10 spare slugs and shells, while a massive 300 rounds of assault rifle ammo would fit in the same space.
Of course, the thing is only ever used by civilian militia, so the fact that it sucks is kind of the whole point of its inclusion, but still, it's hard to ignore just how much it pales in comparison to the other weapons.
Fun fact, the gun's real name is TOZ-34, and it appears in STALKER: Shadow of Chernobyl (all of its assets are in the game but it can't be found anywhere, most mods add it) and its prequel - Clear Sky.