Is there a way to keep my twitter off google, and still have a public account?

[The Gold Fighter]

My name is really unique, so the search results are already pretty limited when someone googles me. I right now have a private account on twitter to prevent things from showing up on google. But it's really annoying because I can't get retweeted as easily. It actually impedes on how I use twitter since I want more people to see my tweets.