1. I created a new field in Configure Call Form
2. Name: Affected User
3. Type: Reference
4. Table to Reference: sys_user
5. Clicked Add.

This created the field I need. Though I do not believe this is the right way to do it and that Affected User has to be an OOB field in some version of ServiceNow or it would not have so many references in the community posts. 

Thanks everyone, now I am trying to figure out why the Caller field set to Mandatory only flashes the Red Asterisk next to the field name, then the asterisk disappears.