No documents are needed to get renters insurance. Because you can buy it online, all you really need is your credit card. Some insurers may ask for your social security number, but the bottom line is that insurers aren’t going to make you submit any documents to buy renters insurance.
However, you should consider creating a renters insurance home inventory before purchasing renters insurance in order to know exactly how much personal property coverage you should buy, and make it easier to file claims if disaster strikes in your rental.