That depends: Do you have the licenses for each track you will be using?
The licenses that you need are similar to what you would need just to play music in the background. They are the mechanical, master use, and sync licenses. So you could potentially use the catalogs from licensed music providers (such as Monstercat, Bass Rebels, ArgoFox, Pretzel, or StreamBeats) assuming that it does not violate the Terms of Service for that company.
Twitch’s Terms of Service specifically state that Live DJ sets are not permitted unless all content is properly licensed.