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.
On second thought (again, not enough info to be sure), you may want to start off by checking who the author is for that page. If you just changed the name of the original sample page it may not show up as you being the author of that page. There may be other reasons why you would not be listed as the author as well.
So WordPress SEO should be assigning all of your posts/pages with you as the author. Since you’re saying all the other pages are fine, it may just be a simple matter of checking to make sure YOU are listed as the author. If you are not, change that and try again.
Even easier:
There’s a setting for this under SEO > Social in the plugin.
Go to
[yoursitehere.com]/wp-admin/admin.php?page=wpseo_social#top#google
In the “Author for homepage” dropdown:
Choose the WordPress user you’d like to set as an author for the homepage. Make sure the Google+ URL is set in that users’ Profile settings.
Give that a try and let me know if it works. 🙂
