If you read the bill they do need a warrant to track your internet activity (though they aren't really tracking that, the requirement is that a provider of IP addresses keep records of who was in possession of that IP address; nothing about what you're doing with it; though if you have records of that as well they can be required as well).
It would require that you keep the records but the relevant section of statute (
Title 18, Section 2703) still requires a warrant (if the possessor of said information isn't willing to hand it over) or subpoena for the government to get the information.