Linking an image or word to a "Like"

No, there's no way to do exactly what you're looking for. It *is* possible to create a custom Like button/text link using Open Graph Actions. That Like button can only be for a page on your site though, not for a Facebook Page. Open Graph Actions are Facebook application specific 'actions' that users can take on your site, but (again) it has to be for a specific URL for your site, not any other URL.

I hope that helps answer your question. One other option you may want to do is something like:
"If you like this website please {JFBCLike href=https://facebook.com/your-url layout=button_count} us on Facebook"

That will create a Like button for your Facebook Page in the URL. It will use the standard Facebook Like button though, but it would still have the same effect. Also, since it's a familiar button, it may work just as well or even better than a link that a user may not know what will happen when they click it.

Hope that helps,
Alex

Glad to help. As always, if you need anything else, just let us know.

Thanks,
Alex