Is there anything I can do about my landlord requiring me to declaw my cat?

Did the lease you signed state that any cat you have must be declawed or is this something they are trying to add after the fact? If the lease states they must be declawed then your choices are to move, discuses it with the landlord and offer to sign a contract saying you are responsible for any and all damage done by the cat as due to it not being declawed with an additional refundable pet deposit up front (they may or may not take this offer), show them documentation about declawed cats having a tendency toward litter box avoidance (causing even more damage to their property), or have the cat declawed. They are under no obligation to accept any of your "offers" and if the do get it in writhing. If it is something they are trying to add after the fact and it is not on the lease then you are under not obligation to do so, they can't enforce something that is not in the lease.