How can I move a tag on a git branch to a different commit?

Use the -f option to git tag:

-f
--force

    Replace an existing tag with the given name (instead of failing)

You probably want to use -f in conjunction with -a to force-create an annotated tag instead of a non-annotated one.

Example

1. Delete the tag on any remote before you push

   git push origin :refs/tags/<tagname>
   

2. Replace the tag to reference the most recent commit

   git tag -fa <tagname>
   

3. Push the tag to the remote origin

   git push origin master --tags
   

To sum up if your remote is called origin and you're working on master branch:

git tag -d <tagname>                  # delete the old tag locally
git push origin :refs/tags/<tagname>  # delete the old tag remotely
git tag <tagname> <commitId>          # make a new tag locally
git push origin <tagname>             # push the new local tag to the remote 

Description:

• Line 1 removes the tag in local env.
• Line 2 removes the tag in remote env.
• Line 3 adds the tag to different commit
• Line 4 pushes the change to the remote

You can also change line 4 to git push origin --tags to push all of your local tag changes/updates to the remote repo.

The above answer is based on content in the question by @eedeep, as well as answers by Stuart Golodetz, Greg Hewgill, and @ben-hocking, and comments below their answers, and @NateS's original comments below my answer.

More precisely, you have to force the addition of the tag, then push with option --tags and -f:

git tag -f -a <tagname>
git push -f --tags