Williams, 18, who can play in midfield or defence, joins fellow Iron player Rory Coleman at York Street.
Paul Hurst, joint manager of the Pilgrims, said: "He is highly thought of at Scunthorpe United and his move has come about through contacts we have there.
"He is primarily a midfield player who can also operate at right-back and hopefully he will develop with us.
"He's comfortable on the ball and we have perhaps been missing a little bit of creativity in that area."