In Destiny, siva offerings are new consumable items that can be used to start a public event in Archon’s Forge. You can earn them by completing Patrol missions, story missions, and Rise of Iron strikes that contain SIVA enemies. They also drop as basic engrams. Players can only hold one at a time, and they can either use it or transfer it to their vault to get another. They can also find them at random from enemy kills in the Plaguelands or as a reward from completing Weekly Bounties.
Once a player has a SIVA Offering, they can head to Archon’s Forge and interact with the terminal that appears over the observation deck just before dropping into the arena. This will trigger the event and reward the player with unique Archon Forge loot, including Legendary Class items.
Rewards appear to be completely RNG, and the player who activated the event has the highest chance of earning a specific piece. It’s also worth noting that the difficulty of the event doesn’t seem to have any effect on the odds of receiving a high-level loot item.
It seems that the best way to farm these items is to simply patrol the Plaguelands, killing enemies as you go. A few of the most notable spots include the area just across from where you spawn in the Rocket Yard, and inside the room with the hole in the wall and sensor grid. The Splicer Captains that drop there have a particularly high drop rate, and they can sometimes spawn a Brood Mother when killed.