There are prepaid cards in almost every US grocery and convenience store, typically Mastercard and Visa. They don't require any ID to buy and have a fee around $5. Most can't be reloaded.
Of course if you were setting up an illegal hidden service payment would be the least of your worries. Moving it around every few weeks inside Russia like the inter-dimensional dark fortress in Krull to prevent long term traffic analysis, maintaining your site from a moving location everyday, and making sure you don't blow opsec giving away your identity is probably more difficult than finding creative methods to pay for hosting.