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Scapegoating?

From Wikipedia:

Scapegoating (from the verb "to scapegoat") is the practice of singling out any party for unmerited negative treatment or blame as a scapegoat. Scapegoating may be conducted by individuals against individuals (e.g. "he did it, not me!"), individuals against groups (e.g., "I couldn't see anything because of all the tall people"), groups against individuals (e.g., "Jane was the reason our team didn't win"), and groups against groups.

A scapegoat may be an adult, child, sibling, employee, peer, ethnic, political or religious group, or country. A whipping boy, identified patient or "fall guy" are forms of scapegoat.

On many occasions, scapegoating does rely on the accuser's guilt.

To frame someone

25. Informal. to incriminate (an innocent person) through the use of false
    evidence, information, etc.

(dictionary.reference.com/)

Wiktionary has

blameshift verb (biblical)

To blame another for one's own wrong-doing. Blameshifting ... pointing
the finger at another when trying to save one's skin.

Dictionary.com only gives the noun:

blameshifting noun

the act of transferring responsibility for an error or problem to
another; also written blame shifting

Not quite what you want perhaps: a misdirect, a diversionary tactic used by magicians.

I can't find a good dictionary definition of this usage, but
Wikipedia
defines it for magic, and
The Guardian
uses it well:

Bankers, bosses, selfish politicians; all are masters of misdirection. It allows them to escape blame-free.

Dictionary.com:

a wrong or incorrect direction, guidance, or instruction.

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.

The psychological term for this is 'projection'.

Psychological projection is a theory in psychology in which humans defend themselves against their own unconscious impulses or qualities (both positive and negative) by denying their existence in themselves while attributing them to others. For example, a person who is habitually rude may constantly accuse other people of being rude. It incorporates blame shifting.

slander

Slander is the act of making a false, negative spoken statement about
someone. Words falsely spoken that damage the reputation of another.

In law, the word slander is contrasted with libel, which is the act of making a false written statement about someone.

If you misrepresent or malign someone, particularly in a public way,
that's a hatchet job.

hatchet job (n) : a false accusation of an offense

(vocabulary.com)

How about --

red herring: to intentionally mislead or deceive.

perhaps "the pot calling the kettle black"

How about Impute?

From Merriam Webster:

Verb im·pute im-ˈpyüt

1. to lay the responsibility or blame for often falsely or unjustly

Was also thinking about inculpate, but impute seems a better fit.

Your edit sounds a little like a tu quoque, a Latin phrase that is sometimes used in English. It literally means "you, too." If someone accuses you of something that you're actually guilty of, and your only defense is to point out that the accuser is guilty of the same thing, that's a tu quoque. It's considered a logical fallacy if you think someone else's guilt absolves you of your own guilt.

sub·ter·fuge
/ˈsəbtərˌfyo͞oj/
noun
noun: subterfuge; plural noun: subterfuges

deceit used in order to achieve one's goal.
_{Oxford Dictionaries}

I would use the word demagogue or demagogy for this act as politicians are mentioned. I am also in favor of Red herring.

How about fabricate?

From Oxford Dictionaries:

Invent (something) in order to deceive:
‘officers fabricated evidence’

synonyms: forge, falsify, fake, counterfeit

Counterfeit may also be suitable here.