The V3 API mentions branches in its reference page

The ref in the URL must be formatted as heads/branch, not just branch.
For example, the call to get the data for a branch named sc/featureA would be:

GET /repos/:user/:repo/git/refs/heads/sc/featureA

Create a Reference

POST /repos/:user/:repo/git/refs

Parameters

ref

String of the name of the fully qualified reference (ie: refs/heads/master). If it doesn’t start with ‘refs’ and have at least two slashes, it will be rejected.

sha

String of the SHA1 value to set this reference to

So it should be possible to create a new branch, by naming a new '/heads' in the ref parameter.

Potherca points out to a working test, using the service of www.hurl.it (which makes HTTP requests)

• Find the revision you want to branch from.
  Either on Github itself or by doing a GET request from Hurl:

  https://api.github.com/repos/<AUTHOR>/<REPO>/git/refs/heads

• Copy the revision hash

• Do a POST request from Hurl to https://api.github.com/repos/<AUTHOR>/<REPO>/git/refs with the following as the POST body :

    {
        "ref": "refs/heads/<NEW-BRANCH-NAME>",
        "sha": "<HASH-TO-BRANCH-FROM>"
    }
  

  (obviously replacing the <NEW-BRANCH-NAME> with the name your want the new branch to have and the <HASH-TO-BRANCH-FROM> with, you know, the hash of the revision you want to branch from)

  You will need to use HTTP basic and fill in your Github credentials to access the Github API.

• Press the Send button and your branch will be created!

In 2022, you can also use gh api

gh api \
  --method POST \
  -H "Accept: application/vnd.github.v3+json" \
  /repos/OWNER/REPO/git/refs \
  -f ref='refs/heads/featureA'
 -f sha='aa218f56b14c9653891f9e74264a383fa43fefbd'

You don't need the refs/ prefix in that API. Looking at the docs, it says that:

Returns a single reference from your Git database. The :ref in the URL must be formatted as heads/ for branches and tags/ for tags.

So if you change your step to the below, it should work.

- name: Create tag
  uses: actions/github-script@v3
  with:
    script: |
      console.log(await github.git.getRef({
        owner: context.repo.owner,
        ref: "tags/v0.0.1",
        repo: context.repo.repo,
      }));

NB: You're using github-script version 3, but there's already v5. If you want to keep your actions up to date, I previously described how that can be done using dependabot: https://stackoverflow.com/a/70196496/1080523

https://docs.github.com/en/rest?apiVersion=2022-11-28 is correct.

Please a have look the left sidebar REST API reference

After hours of debugging, I finally find that apparently it's erroring because I'm pushing a GitHub workflow!

The solution was to add the workflows scope to the OAuth token.

Yes @Siddharth,

The way to do it is as you pointed. I found this good explanation in StackOverflow: Github API - create branch?

Also, using Octokit SDK, you can easily achieve it like this:

octokit.rest.git.createRef({
  owner,
  repo,
  ref,
  sha,
});

docs here: https://octokit.github.io/rest.js/v18#git-create-ref