I agree with Avon that "frame" (or "frame up") is the best short term for the tactic that the OP asks about. A longer phrase that suggests the same thing is "set [someone] up to be the fall guy." Although a "fall guy" in some instances is a willing participant in a conspiracy to obstruct justice—pleading guilty to a crime in order to let others off the hook—when "fall guy" is linked to the verbal phrase "set up," the usual sense of the expression is that the fall guy is an unwitting dupe or scapegoat of the actual criminal or criminals.
A Google Books search for the phrase "set him up to be the fall guy" finds a number of fairly recent matches, all in the above sense. Some examples: From Margaret Daley, Security Breach (2015):
Selena nodded. “But Sid Huntington insists he's innocent, that someone set him up to be the fall guy, and Michael believed him.”
From Diana Kaye, The Power of Trust (2013):
He was fully absorbed in his own cleverness, by now: "I've done it before. I can make it look as if you've been a victim. It's simple; really; just a matter of planting evidence and letting the right people know where it is. I can forge anyone's handwriting; too, that'll come in handy. Leave it to me; I can make anyone appear guilty as Hell. We'll need someone to put the blame on, though ... Hey, I've got it! Rob, he'll do! I can set him up to be the fall guy ... what are you doing?” She'd pushed him away, violently.
From James Campbell, Southern Gold (2011):
Slim laughed softly. "What's going to happen hen your cop boyfriend finds out that he has been misled by you all along? Wonder what he's going to think about you when he learn that you and his brother set him up to be the fall-guy if the shit really hit the fan?....I'm just wondering, when will you really tell him that the joke is on him?”
From Jeff Blackburn, Huitt's Trail (2010):
Dwayne Reed had been a childhood friend, who followed the boys everywhere. Reed was a simpleton, who did everything that the boys told him to. They in turn had treated Reed with great contempt, they teased him, and set him up to be the fall guy for all their devious pranks. Reed believed the boys to be his only friends and had followed them down the path to wrongdoing.
From David Rosenfelt, Bury the Lead (2007):
"Lassiter, whether on his own or with Eliot's approval, murdered the other women to deflect attention from the main target, Rosalie. Then, to get revenge against Daniel, Lassiter set him up to be the fall guy. I'm sure he found it fit together quite well.”
From H. Paul Jeffers, History's Greatest Conspiracies (2004):
More than seventy years after Bruno Richard Hauptmann was executed for the kidnapping and murder of the two-year-old son of aviation hero Charles A. Lindbergh, some students of what was known as "the crime of the century," which the famed muckraking journalist H. L. Mencken termed the greatest story since the Resurrection of Christ, believe that Hauptmann was in fact the victim of a conspiracy involving faked evidence to set him up to be the fall guy.
From Jan Delasara, PopLit, PopCult and The X-Files: A Critical Exploration (2000):
There is, however, another possibility. The intelligence forces of the Parallax Corporation may have been aware that Frady was investigating the group, and then simply set him up to be the fall guy for yet another political assassination.