- Microdata is an extension of HTML5. It’s "just" five new attributes and "some" rules.
- Tumblr allows editing your theme’s HTML.
- Tumblr allows adding HTML to your posts.
So yes, you can use Microdata in a Tumblr blog.
(Note that you may also use other syntaxes than Microdata. Schema.org is a vocabulary and works also with RDFa Lite, for example.)