Frankie - what has been your landlord's repsonse thus far?
Has he or she refused to call in an exterminator?
Read your lease to see if this is mentioned.
Are the rodents you are referring to mice?
Mice are hard to control, especially with this terrible weather we are having - they don't like snow either, and it doesn't take much of an opening for them to squeeze through!
While trying to work it out with your landlord, in the meantime - look to see if there are any openings you can seal up. Try buying a package of mouse bait (they sell little crystals in a plastic container - try Home Depot - - the mice nibble on it, go to find water, and die). They also sell sticky paper traps. I had this issue with a listing of mine - the owners were out of state, so I was the one to leave the traps and bait in the basement and garage - problem solved!
I've attached a link to the NJ Landlord Tenant law which would pertain to this. I agree with Mike that this is likely and area the landlord is responsible to maintain for health and safety. Read over the link and when you contact the landlord you can address chapter and verse what you have the right to expect.