Check your purchase agreement. It's in there.
However, very likely yes. Often, the amount of fuel is calculated and that cost is paid by the buyer.
Now, if it's truly, honestly not in there . . . . then (and I'm not a lawyer so this isn't legal advice) perhaps not. It'd be like buying a house with boxes the seller left in the attic. You're buying the property and everything in it.
But oil in the tank is handled sort of similarly (roughly) to taxes that the seller may have already paid on the property. Let's say the seller paid half a year's property taxes on July 1. At closing, the seller gets reimbursed for the amount of taxes paid that are applicable after your purchase of the house.
So check the contract. And certainly ask your own Realtor. (Uh oh. You DO have your own Realtor, don't you?). Don't rely on the listing agent for such advice.
Hope that helps.