RE: Running workflow as user initiating the workflow
Yes surely you can do that if the following conditions are met
1. User creating phone call shall have privilege to create case.
If above condition is met,
2. You can create the case with the same user who created the phone call.
Alternatively, you can user assign action in workflow and assign the case after creation to the owner of phone call.
In the workflow steps, use "Assign Record" action.