Yes, but you need to obtain permission, and will have to pay a royalty if money is going to be made from it. I suggest you go to http://www.songfile.com/ and read up on this matter for yourself. Also check out the Harry Fox Agency at http://www.nmpa.org/hfa.html. There are many factors involved, such as how the song(s) are going to be sold and distributed. In general, permission is required from the artist or publisher before you can record and distribute a cover tune. From the looks of it, the cost is minimal depending on how many units you plan to sell or distribute.

may I record a song written by another composer?