I noticed that my first paycheck from my new job has FICA taxes under withheld. Who should I to talk to about resolving this issue?

You talk to your supervisor or human resources, unless you have direct access to someone in payroll. It sounds like a problem with the payroll software.

Payroll dept., but it is highly unlikely that FICA and Medicare would be wrong. FICA is 6.2% and Medicare is 1.45%.

Of course it does. What's the issue? Putting exempt on your W-4 just affects income tax, not FICA

Since you are the same person who keeps asking about the FICA exemption for college students, I will repeat my previous advice: TALK TO PAYROLL.

What issue exactly do you want to resolve?

Everyone who gets a paycheck has those taxes withheld.

If you have questions about the amount, talk to your supervisor or Human Resources department.