So… let me start by saying there are probably a couple of ways of doing exactly what you are asking. One would depend on the theme you are using and the other would require you to get into your header in _____.php file. Since you’re asking this question, I’m going to assume you don’t play around with that and I wouldn’t recommend it anyways.
Instead, I would recommend you DO NOT put this in your header file. It will probably work just fine, but may have some unintended consequences if you have more than one person posting on your site. You didn’t include a website or enough information to really give a more specific answer. So here are my two recommendations:
1) Consider if your homepage really needs authorship markup. It may very well be that your home page is also your blog page and your posts are already marked up. If that’s the case, I wouldn’t bother with it because it’s your posts you’re trying to drive traffic to and your homepage is somewhat irrelevant in the scheme of things. It’s also never likely to rank higher on anything than your posts because you aren’t tailoring SEO for the page.
2) If you have a landing page as your home page, then the simplest answer would be to put a catchy line like the following into the text editor: <a href="https://plus.google.com/"your number here"?rel=author">Check me out on Google+</a>
Hope that helps.