Well, here we are…227 years after the Declaration of Independence… however. I reject the “Republic for which it stands”, and I also reject the constitution.
In short, I remain a loyal subject of the Queen, Her Majesty Elizabeth II. My passport says “American Citizen”, but since I do not accept the validity of the treasonous constitution, what does that make me?
Shall I start paying my taxes to the “inland Revenue”? And, more importantly, since my objection means that (to me) Washington, Jefferson, Adams, et.al. are all a packof traitors, do I have to celebrate their birthdays?
Anybody know what my legal status is?
Incompetent to stand trial?
Please read “The Man Without A Country” for further details.
But seriously, there have been many threads about renouncing your citizenship and Cecil has answered the question also.
I believe that you are going to have to leave the country to accomplish such a task.
Move up here? 
Criminally insane?
What you think you are is not important. What counts is what you actually are. If you’re born in the US, you’re a US citizen, no matter what you think about the Washington usurpators’ legitimation in governing what you think to be a British colony. You could of course renounce your American citizenship and apply for the British one, but as long as you haven’t formally done so you’re American, albeit one who thinks he’s British, and American authorities won’t do you any harm as long as you obey American law and pay your taxes.
Especially the taxes.
Dude, it’s a free country! You can wear sackcloth and ashes on Presidents’ Day if you want to!
It should be noted that the United Kingdom (Her Majesty’s Government) continues recognition of the government of the United States of America as a legitimate and legal government, a policy that at the very least dates to the resolution of the War of 1812, although first stated in the Treaty of Paris. Thus, whatever the legality or lack of the original rebellion, Her Majesty’s Government now sees fit to admit to the legality of the current situation. Therefore, if you are truly loyal to Her Majesty’s Government, you will go along with the policies, thereof.
Well, no, actually. As Dogface notes, King George III relinquished all claims to the territory of the United States back in 1783, in Article 1 of the Treaty of Paris, on behalf of himself and his successors. You can’t just declare yourself to be a British subject. If you weren’t born in British territory, or of British parents, you can’t claim status as a British subject. You’d have to apply to emigrate to the U.K.
There were several court cases in both the U.K. and the U.S. in the years following the Treaty of Paris that raised this issue. The consensus of both the American and the British courts was that Americans who wanted to remain British subjects had to leave the U.S. within a reasonable time after the peace treaty. By doing so, they never acquired American citizenship. Those who stayed acquired American citizenship and ceased to be British subjects.
The ones who left became the Loyalists, for example in New Brunswick and Upper Canada.