The 23-year-old midfielder was signed a year ago after being released by Hull City, but an ankle injury restricted him to only 13 league starts last term.
"It's been a frustrating few months with the injury but I am 100% fit now," he told Crawley's website.
"It [the contract] gives me the opportunity to hit the ground running in pre-season and hopefully impress the manager enough to get another one."
Henderson, who began his career at Arsenal, played only one first-team game during his year at Hull and was loaned out to Stevenage.
"This is a fresh start for Conor," said Crawley manager Mark Yates.
"I know he has a lot of ability and he has the chance now to show what he's about."
Conor Henderson has agreed a new six-month contract with Crawley Town.