Snowden, 37, fled the United States and was given asylum in Russia after leaking secret files in 2013 that revealed vast domestic and international surveillance operations carried out by the U.S. National Security Agency where he was a contractor.
"After years of separation from our parents, my wife and I have no desire to be separated from our son. That's why, in this era of pandemics and closed borders, we're applying for dual US-Russian citizenship," he wrote on Twitter.
His lawyer in Russia said last month that Snowden had been granted permanent residency rights.