MTG: Death Cultist + Carrion Feeder?

Quick question. In Magic: the Gathering, can I use Carrion Feeder's ability to sac a Death Cultist and reap the benefits of both cards' abilities? In essence, this would, in a single move, allow me to gain a life, have an opponent lose a life, and place a +1/+1 counter on Carrion Feeder.