Yes, absolutely! While there are many iPhone screen repair shops on the island, there are very few for Android. This is quite odd, especially as Android does have quite a large market share.
There is a shop called S-Phone, located inside Goodwill (link to the
Places page below), that fixes Androids. They service Android screen repairs as well as other issues that you might have with your device.
However, they only fix certain models. It'd be much better to go in and show them the phone to see if they fix that particular one or not or have someone who speaks Japanese to call in advance as their English is quite rusty, but they will be welcoming like all other shops on Okinawa—though it's recommended to bring a(n electronic) translator along.
If S-Phone can repair your phone, they will have to send it to the factory which will take approximately 2 weeks. Your phone will be returned, repaired, but all data will be wiped so it's best to make a backup before taking it in if you don't want to lose it.
Goodwill is a unique electronics store that mainly specializes in computers, computer peripherals and computer accessories.