The London-born 23-year-old joined the Reds after spending two years with Turkish Premier League side Alanyaspor.
Tursun was one of 17 new arrivals at the West Sussex club this summer.
"Alper has had a good offer to play in Turkey and it's been mutually agreed he can leave," Reds head coach Dermot Drummy told the club website.
League Two club Crawley Town have cancelled the contract of Alper Tursun just one month after signing the defender on a one-year deal.