Naphta: Not on its own: And not easily.
A rocket works by rapid creating a large volume of gas, and expelling it in one direction, thus gaining thrust in the opposite direction.
The creation of this gas usually involves a Fuel, and an Oxidizer burning together.
In the case of gunpowder, this fuel (charcoal) and oxydizer(saltpeter) is pre-mixed, along with some other stuff to facilitate ignition and smooth burning.
Naphta is a most excellent fuel for a rocket, but it lacks a suitable oxidizer. Yes, it can burn with the Oxygen in air, but now you are trying to burn a liquid with a gas, to form a controlled explosion. Very possible, it is exactly what any airliner does, but not easily achievable without some very complicated machinery.
Mixing it with a solid oxidizer is just not on. Yes making a clay-like mixture of Naphta and Saltpeter, or Naphta and Ammonium nitrate makes a very nice explosion, but not a contained explosion. You have basically invented an unstable form of dynamite.
The only remaining option is to make your Naphta rocket with a liquid oxidizer. Specifically Hydrogen Peroxide.
In our history Hydrogen Peroxide was only discovered in 1818, but the manufacture of the substance is not that exotic, and it is very likely alchemists of the 1200's did discover it, they just had no clue what to do with it. One can also reasonably easily (but very inefficiently!) make Hydrogen Peroxide if you have any form of electrical battery to perform electrolysis.
OK. Now you have your Naphta, and you have your Hydrogen peroxide.
You just need to mix the two liquids together in a strong enough combustion chamber, put a suitable nozzle on it, and you have a rocket. The liquids can be pressure-fed from their tanks, so no worry about fancy pumps or anything.
This would make a rocket using 1200's tech.
A very, very expensive rocket. Not at all suitable for mass production, and too unsafe/unstable for broad military use.
You would get an even better rocket by using concentrated Nitric Acid as your oxydizer.. But that stuff is *nasty to handle, even with modern tools.