Can you be arrested without a search warrant?

Yes, if the LEO observes you in the commission of a crime and/or has probable cause. Warrants are generally only required for crimes not observed by law enforcement, but after sufficient evidence (or probable cause) has been obtained through investigative or forensic work.

Added: Also - if you are 'wanted' on a warrant and the LEO sees and identifies you as the wanted subject, they do NOT need the warrant in their possession to 'serve' it and arrest you on the spot. Their mere knowledge of its existence is sufficient.