Since a few months ago this is possible using gitlab-runner:

gitlab-runner exec docker my-job-name

Note that you need both docker and gitlab-runner installed on your computer to get this working.

You also need the image key defined in your .gitlab-ci.yml file. Otherwise won't work.

Here's the line I currently use for testing locally using gitlab-runner:

gitlab-runner exec docker test --docker-volumes "/home/elboletaire/.ssh/id_rsa:/root/.ssh/id_rsa:ro"

Note: You can avoid adding a --docker-volumes with your key setting it by default in /etc/gitlab-runner/config.toml. See the official documentation for more details. Also, use gitlab-runner exec docker --help to see all docker-based runner options (like variables, volumes, networks, etc.).

Due to the confusion in the comments, I paste here the gitlab-runner --help result, so you can see that gitlab-runner can make builds locally:

   gitlab-runner --help
NAME:
   gitlab-runner - a GitLab Runner

USAGE:
   gitlab-runner [global options] command [command options] [arguments...]
   
VERSION:
   1.1.0~beta.135.g24365ee (24365ee)
   
AUTHOR(S):
   Kamil Trzciński <ayufan@ayufan.eu> 
   
COMMANDS:
   exec         execute a build locally
   [...]
   
GLOBAL OPTIONS:
   --debug          debug mode [$DEBUG]
   [...]

As you can see, the exec command is to execute a build locally.

Even though there was an issue to deprecate the current gitlab-runner exec behavior, it ended up being reconsidered and a new version with greater features will replace the current exec functionality.

Note that this process is to use your own machine to run the tests using docker containers. This is not to define custom runners. To do so, just go to your repo's CI/CD settings and read the documentation there. If you wanna ensure your runner is executed instead of one from gitlab.com, add a custom and unique tag to your runner, ensure it only runs tagged jobs and tag all the jobs you want your runner to be responsible of.

Unofficial alternative gitlab-ci-local

There's an unofficial package which looks promising, with more features than the official gitlab-runner exec: https://github.com/firecow/gitlab-ci-local

It allows you to run gitlab pipelines locally as shell executor or docker executor.

gitlab-runner exec works as its own standalone command and runs the job in the context of where the executable is called -- it will not cause the job to be run on a registered runner. It is solely a local operation, so you must have the binary available.

You can run gitlab-runner exec inside of your runner container or a new container if you want.

For example (assuming Linux platform):

docker run --rm \
       -v $(pwd):/workspace \ # mount directory to the container
       --workdir /workspace \ # set working directory
       -v /var/run/docker.sock:/var/run/docker.sock \ # enable docker
       --privileged \
       --entrypoint="gitlab-runner" \ # set entrypoint
       gitlab/gitlab-runner:latest exec docker MY_JOB

Or use doker exec to run the command on your existing container:

docker exec -it my-running-container-name gitlab-runner exec docker linting

Though, you will want to make sure the .gitlab-ci.yml file and project files are present in the container when you start it...