Tumblr does not give you a specific tool that allows you to rearrange your Tumblr posts, but you can adjust what posts appear on the main page if you edit the date that the posts were added. When you edit the post to today's date, the post is sent to the front page of Tumblr. This function is useful if you want to feature older posts, or an important post is listed farther back in your archives than you would like it to be.
Click the "Edit" icon next to the Tumblr post that you want to rearrange.
Select the "Date" field and select a new date to move your Tumblr post.
Click "Save Changes" to move this post on your live Tumblr blog. Repeat for each post that you want to rearrange. Coordinate the date changes of each post so that all posts appear in the order that you want them to.