The 20-year-old has yet to feature for the Palace first team, having moved to the club in September last year after beginning his career at Cardiff City.
Spence, who has also spent time on loan at Welsh side Barry Town, scored seven goals in 15 games for Crystal Palace's under-23 side last season.
He is the eighth player to move to League Two Rovers in this summer.
"We are hopeful he can come here, make the transition into senior football and have a positive season with us."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!