Twitter has a high Google search rank, so chances are, your profile will show up in a Google search. Depending on the degree to which this bothers you, you can do several things:
Keep in mind that the words you write in updates may also be indexed and come up in a search for those terms.
Here's how:
You may be required to log in to your Google account. If you don't have one, you may need to create one. More information about removing your content from Google's search index is here.