Yes. South Seas Island Resort has a walkable Par 3, 12-hole short course called The Clutch, located at the resort’s North Pointe on the Gulf. The course is open to members of South Seas and those booking directly with the resort Tuesday through Sunday, 8:30 a.m. to 5 p.m. Titleist clubs are available to rent, and hand carts and golf carts are on-site, though availability can be limited.
If you’re after a standard golf experience, Sanibel Island is a short drive across the causeway and has three options: The Dunes Golf and Tennis Club (public), The Sanctuary Golf Club, and Sanibel Island Golf Club.
Sources: Capturing Captiva, South Seas (link)

