Yes, you can. However, you may need to get permission from the original copyright owner in some of the countries in which you plan to release your cover version. This permission would typically take the form of a mechanical license. In the U.S. you can purchase a mechanical license from The Harry Fox Agency.
Also, it is very important that no one is misled into thinking they're buying or listening to the original so you must not include the name of the original performing artist anywhere in the release information. That means when you're filling in your track and artist details don't credit or reference the original artist. As an example, using the track title ‘Club Tropicana’ is fine but using ‘Club Tropicana (Wham)’ or ‘Wham Original – Club Tropicana’ would mean that your cover would not be able to be delivered to the digital stores. We want everyone to hear your covers so please help us with this.