The skull is a mind weapon. It will open a new frontier of psychic warfare. It was Stalin's dream.Irina Spalko talking about Stalin.
Joseph Stalin is the posthumous overarching antagonist of the 2008 action-adventure film, Indiana Jones and the Kingdom of the Crystal Skull, the fourth installment of the Indiana Jones franchise. He is the former leader of the Soviet Union, and despite having died years before the film, his actions shaped most of the events of the plot, especially involving the film's main villain Irina Spalko.
It can be assumed that most of Joseph Stalin's history is similar to his real-life counterpart. During World War II, Stalin was worried about Adolf Hitler, so he had the Soviet police turn a blind eye to Nazi's atrocities. This allowed Colonel Klaus Kerner to steal a copy of the Hermocrates from a Leningrad museum in 1939 and leave unhindered.
Stalin eventually turned to experiments to explore the human mind and psychic capabilities out of an effort to win the Cold War as he was worried about the United State's nuclear capabilities. Eventually, presumably during his experiments, he found out about the 1947 crash in Roswell, New Mexico and its ties to the legend of the Crystal Skull.
So in order to find the Crystal Skull, Stalin brought in Irina Spalko to find it, which he intended to use to brainwash American troops so he could win the Cold War. Though unfortunately for Stalin, he died on March 5, 1953, never finding the Crystal Skull.
Despite Stalin's death, Irina Spalko continued to pursue Stalin's dream in the years following his death and, eventually during the events of the movie she was able to find the Crystal Skull, but unfortunately for her, it killed her and the Soviets were never able to use it to win the war.