My partner has a wart on his penis?

What kind? Most genital warts are caused by HPV virus and you could get genital warts as well. Using a condom does not protect against HPV, even if the wart is covered by the condom. An other question is, "What other sexually transmitted infection(s) does he have?"
Get checked. Penile warts can grow and can spread to you. They can either freeze, cut, burn or prescribe aldara (imiquimod). Good luck get his penis examined by a physician.
He needs treatment. by a urologist or dermatologist and you need 2B checked by your gynecologist. Genital warts are very infectious. Wart came from his or someone else hand or by sexual contact from you or someone else.