set up a twitter account and dont link it to your real name. sign up through a vpn, say waht you want and dont worry about it. unless what you say is actually illegal no one can really track you down without getting your login IP address from twitter. People get tracked down because they link it to their PSN/XBOX/FB account or reuse usernames between twitter and somewhere else they have left personal details.
I have a twitter accout that I set up through TOR and a VPN. I use a username I have never used elsewhere. I dont post anything controversial but I would be pretty happy that I could not be traced without someone obtaining a court order requiring twitter to hand over my IP address, even then it would point to a VPN that (supposedly) does not keep logs.