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What do we call "a person who blames others for things they didn't do"?

I searched on the web, and found the word "blamer". I know what it means, and I don't find it fits the definition I wrote.

Update: It can mean "false accusation" and/or "When somebody says that another did something (wrong) when they haven't".

There is a related word, scapegoat, which means:

scapegoat (noun) A person who is blamed for the wrongdoings, mistakes, or faults of others, especially for reasons of expediency.

From this word, we have the word scapegoater, which means:

scapegoater one that makes a scapegoat of something or somebody

While scapegoat is fairly common in the vernacular, I think scapegoater is a less common word. However, it fits what you are looking for.

Here's a usage of it in print:

Tolerance and independent thinking are essential to a democratic form of government, but the scapegoater cannot think straight.

(Charles Henry Scherf, Do You Own Thinking, 1946)

Another book about hostilities in the workplace says:

A scapegoater is one who transfers blame to persons or groups, who are not necessarily guilty, in order to focus attention away from those who are actually responsible — sometimes from themselves.

(J.A. Wambach & R.W. Fuller, Battles between somebodies and nobodies: stop abuse of rank at work and at home, 2008)

I found imputer.

Noun[edit]

imputer (plural imputers)

One who imputes.

Impute, as a verb, means:

1. to attribute or ascribe (something dishonest or dishonourable, esp a criminal offence) to a person

Note: I am not a native speaker, so I can't comment on how commonly it's used.