After being transplanted with the arm of a recently executed bandit, a shy and coward farmer must learn how to control his new body part and overcome his cowardice when a violent gang led by the bandit’s vicious brother threaten the town and the woman he loves.

Why does it matter that the protagonist is a farmer ?

What you’ve described is “a peace loving ethical” person who must behave in an adverse way to his usual values and strength of character or stand witnessing the destruction of his town and possible murder of his girlfriend.

If you weave these aspectS of the story into a 30 word summary, you’ll achieve a much stronger log line.

A small Western town circa 1880's/1890's.
Actually, it's an action comedy with a steampunk weird western comic or pulp magazine feel, as 'Jonah Hex' or 'Wild Wild West'.

It's a struggle. His body is adapting to his new arm and viceversa. The arm is trying to gain control of the rest of his body, such as in 'Orlac's Hands' - the German expressionist classic - and 'Body Parts' - the early 90's horror movie.

Haha! I like it.
The working title so far I've managed to come up with is 'Armed' - I know, it's not so creative but I'm a bit weak at titles.

Possible Title: "The Wrong Arm of the Law"

Is the body part controlling him? Otherwise isn’t he just going through rehab? So how does him having the arm make him the person to need to stop the gang

What's the setting both in time and place?