How to fetch all posts using tumblr API or Tumblr Rss feed
You can put this code in your html or php.
<script type="text/javascript" src="http://YourTumblrName.tumblr.com/js"></script>
It fetches the content of your tumblr into a page, but it not very flexible. I'm still trying to get the dates and tags fetched. And the image quality is not as good as in Tumblr...
Use XML or JSON and Tumblr API V1
XML: http://yourtumblr.tumblr.com/api/read/
JSON: http://yourtumblr.tumblr.com/api/read/json
Otherwise, there's probably a WP plugin that can handle the entire proces for you:Example WP plugin