You could use Ansible if :
You have to "deploy" without the need for building/testing. For instance, you could deploy from Ansible Tower or by using command line making it great for static websites, small projects , to name a few.
You could use Jenkins if :
Your deployment process and machine environment is pretty straightforward like Heroku/Iron which is configured outside of your team. A custom script could be written which would do a deploy making it the final step of building ( a chained step).
How could you make them work together? :
An ideal combination is by using Jenkins for building, testing, and for saving artifacts. Next, you could call Ansible Tower for handling the deployment process. In other words, making the Jenkins to handle CI process while Ansible is assigned for handling the machine configuration.
If you want more of the Jenkins, you can checkout this Jenkins Tutorial.
For more of Ansible, you can checkout this Ansible Tutorial.
Have a nice day!