The Copyright Act protects original works "fixed in a tangible medium." This includes any recorded songs, digital or otherwise.
Without permission, any copying sampling or re-mixing of another artist's song constitutes copyright infringement.
In a famous case, Bridgeport Music, Inc. et. al. vs. Dimension Films et. al., a court decided that even a snippet constitutes infringement if the defendant "digitally sampled a copyrighted sound recording."
Licensing ensures a DJ can use a song sample without legal trouble. Contact the artist, publisher or record label to obtain a license.
DJs that write songs have automatic copyrights for those songs in the U.S. Registering songs with the U.S. Copyright Office provides full legal protection.