Avec curl

curl -k -u username:'P@ssw0rd' -H 'Content-Type: application/json' -X GET https://tower.acme.fr/api/v2/job_templates/93/launch/ -d '
{
    "extra_vars": {
        "git_path": "/project/plop",
        "git_user": "gittoken"
    }
}'

Via Ansible

#!/usr/bin/env ansible-playbook
---

- hosts: localhost

  tasks:
    - name: call api
      register: plop
      uri:
        url: https://tower.acme.fr/api/v2/job_templates/93/launch/
        method: POST
        force: true
        force_basic_auth: true
        user: username
        password: 'P@ssw0rd'
        validate_certs: false
        # body_format: form-urlencoded
        body_format: json
        headers:
          Content-Type: "application/json"
        body: |
          {
              "extra_vars": {
                  "git_path": "/project/plop",
                  "git_user": "gittoken"
              }
          }
        status_code: 201

    - name: DEBUG 10
      debug: var=plop

Ou encore

#!/usr/bin/env ansible-playbook
---

- hosts: localhost

  tasks:
    - name: call api
      register: plop
      uri:
        url: https://tower.acme.fr/api/v2/job_templates/93/launch/
        method: POST
        force: true
        force_basic_auth: true
        user: username
        password: 'P@ssw0rd'
        validate_certs: false
        body_format: json
        headers:
          Content-Type: "application/json"
        src: plop.json
        status_code: 201

plop.json

          {
              "extra_vars": {
                  "git_path": "/project/plop",
                  "git_user": "gittoken"
              }
          }

Consulter la sortie : https:<tower-FQDN>/api/v2/job_templates/<job-template-id>/