Hi Michelle!
You certainly may! All Guests of Walt Disney World's Parks are able to use the Disney Transportation System including the buses, monorails and boats.
From the Magic Kingdom you have two options. You're welcome to hop on the Resort Monorail, which will stop at Disney's Contemporary Resort, followed by the Transportation and Ticket Center, and then arriving at Disney's Polynesian Resort.
Alternatively, if you wish, you may choose to take a resort boat launch from Magic Kingdom over to the Polynesian's dock.
Be sure to reserve your tickets for the dinner show as far in advance as you can by calling (407) WDW-DINE or by visiting the Online
Disney Dining Reservations System.
Enjoy Disney's Spirit of Aloha dinner show. It's one of my all-time favourites!
Wishing you a simply Magical time at Walt Disney World!
Kirsten