When setting up a data deployment, there are occasions when the Campaign object is not showing for selection:

For this object to show, you must be a Marketing User on the target org as well as the source org.

This means that the Marketing user checkbox is checked in your user information:

​

Once that permission is set against your user, then the Campaign object will show in your data deployment configuration:

If you already have the data deployment screen loaded when you add the permission to your account, start a new data deployment for the Campaign object to show for you.