The 26-year-old, who made 37 league appearances for the Cards last season, has agreed a one-year contract with the option of a further year.
"He is more than capable of making the step back up to league football," Reds head coach Dermot Drummy said.
"In fact, he will thrive on an opportunity to establish himself again at this level."
Arthur, who has previously had spells at Northampton and AFC Wimbledon, becomes Crawley's seventh signing of the close season.
Meanwhile, 26-year-old midfielder Lewis Young has agreed a new one-year deal with the West Sussex club.
Find all the latest football transfers on our dedicated page.
League Two side Crawley Town have signed midfielder Chris Arthur from National League club Woking.