I rent a camping lot where I have a camper set up. The lot is owned and maintained by the owner of the grounds, who lives there year round as well. Recently my camper was vandalized, all the windows were smashed and the inside was torn up. Is there any way the lot owner would be responsible for this damage and pay for the repairs? There is not written rental contract.

No there isn’t. You should have had insurance on the camper. Very similiar to tenant’s having renter’s insurance to protect their personal property.