Try human resources. If they don't do anything contact OSHA.

Rats carry diseases so it is up to your employer to take care of the health risks that can cause problems. if not done then osha needs to be brought in. your employer will be fined, the workers will have to be examined for health purposes at the expense of the employer and the building will be closed for pest control.

Report it to HR and go see a doctor. If HR does nothing then take it to OSHA. How often do they change your air filters at work or even bleach the system? I do maintenance at my job and I know how nasty it can get if they neglect simple things like that. Could be dust, mold... not to sound weird but can you describe the smell? bleachy, necrotic, fecal? Do you have an office near a bathroom and if so do they regularly flush the sinks? Odd questions but it may help figure out the source.

Like others before me have said..contact HR and if nothing is done...OSHA.
They cannot keep unhealthy/unsafe environments for employees.

HR and then OSHA, most definitely. I cannot stress that enough. o.o

That is pretty ewww...
Yea, my view is like above. Report the stench to HR and go see a doctor. If HR does nothing within 48 hours, report it to OSHA.
In the meantime, spend as little time at your little area as work as possible. Take care of yourself. *offers extra fluffy Persian kitty hugs*