Basic version is "If your army is led by a Drukhari Warlord, you can, when mustering your army, give one of the following Artefacts of Cruelty to a Drukhari Character model in your army."
So if your Warlord is Drukhari, then any one Character in the army can have an Artefact of Cruelty. It doesn't have to be the Warlord who has the relic.
Codex Drukhari, top of page 74.
And of course you can also use the Prizes From The Dark City stratagem to "Select one Drukhari Character model from your army and give them one Artefact of Cruelty."
But only if "your Warlord has the Drukhari keyword".