(This applies to TortoiseGit v1.8.3.0)
Make "Git -> Git Sync" first in the Tortoise context menu. (Note: you may need to shift down when you right-click, depending on how you installed Git Sync to appear in your context menu)
The "Remote Update" button will appear at the bottom below. Do this and it will pull all the new remote branches that are not in your local repository.

After that, you can perform "Git β Git Checkout" as usual, and the desired branch will appear in the list.
It should be noted that the same procedure can be used to inform TortoiseGit about new branches that were created in the remote repository, regardless of whether you were originally created or not.
source share