To latexmk your LaTeX document by GitHub Action just create a .github/workflows/latexmk.yml file:

name: latexmk
on:
  push:
    branches: [ master ]
  pull_request:
    branches: [ master ]
jobs:
  build:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v2
      - uses: yegor256/latexmk-action@0.1.16
        with:
          path: foo
          opts: -pdf
          packages: acmart tikz

Preferrably, you should have .latexmkrc in the foo directory of your repository, which configures the behavior of latexmk. If you don't have special requirements in your project, and just need to compile a .tex file, skip the config, everything should work out of the box.

The options available (provided via the with YAML element):

• path is a relative path of the directory with .tex file(s)
• opts is the options to pass to latexmk
• packages is a comma-separated list of TeXLive package to install

In order to test this action, just run:

$ make test

This should build a new Docker image and then try to use it in order to render a simple test.tex document. You need to have Docker installed.