The main reason for using coal or coke is that it burns in a way that alloys the iron with carbon. Crude oil does not burn but rather, the vapor coming off of it does, this mean you can not just dunk your iron ore into oil and burn it, because the heat would be above the ore. Nor is there a good way to burn oil under iron ore in a way that will allow an interchange of the pertrol's carbon with the molten iron.
That said, the sealed crucible steels that you see in the classical to high-medieval periods did not melt the ore inside of the coal/charcoal, instead they mix powered ore and charcoal inside of a crucible, then heated the crucible from the outside. The fuel can in this case be anything of sufficient heat including burning oil, and the iron will alloy with the carbon from the charcoal to make your carbon steel.
Normally making iron from just charcoal and a high quality iron ore requires about 50-60 parts charcoal and 2 parts iron ore (by weight) to get 1 part refined steel. So, technically you can make steel using just charcoal, but you would run out of trees very fast trying to mass produce steel this way. By using the crucible method, you only need a small amount charcoal. It takes about ~2-3 parts charcoal to 75 parts iron ore (by weight). And the heat can all be had from what is probably going to be your cheaper source of energy: your oil.
The reason this method was no longer used by the industrial revolution was that it leads to more impurities because impurities normally flow out of a bloom as it heats up, or out of the slag vent of a stack furnace whereas a sealed crucible holds them all together in a way that you need to keep the iron completely molten for a period of time while the impurities separate so they can be broken away. This means you need a bit more labor than a stack furnace to get an inferior steel. Even when you remove the silicate and oxygen impurities with a sealed crucible, the sulfur and phosphorus are harder to deal with. For this you need a hot blast mechanism which negates the point of a sealed crucible.
Here you have a world building choice:
A: Mass produce wootz steel
A dig site in Merv from about 900AD shows us that sealed crucible steel could be produced in large batches by putting many crucibles into a large underground kiln. This method would not only work for your purposes, but also helps prevent fuel waste since underground kilns retain heat so much better than their above ground varitiety. While many people claim that the blast furnace was the reason for the steel boom, the much more important factor was actually the invention of better tools for working steel. Industrial era roller presses, die presses, wire gauges, metal lathes, etc. allowed people to skip the very laborious task of hammering steel into its needed shapes. Add to this a mechanical hammer for breaking the impurited away from your pucks, and you can produce very large amounts of damascus steel with very little charcoal. It won't take a temper as well as industrial era steel; so, don't expect as good of impact/vibration resistance or springiness, but it will still suit a wide array of uses.
B: Substitute coke for charcoal in a stack or bloom furnace.
Before the 1700s, this is how steel was normally smelted. While this would be very bad for your forests over any serious length of time, charcoal can absolutely be used in place of coke for mass producing steel. Traditional tatara furnaces are still used in Japan today to produce batches of steel in excess of 1 ton using only charcoal. The steel produced by these furnaces produces small amounts of high carbon tamahagane as is used in Katana making, and the rest is sold for making a wide range of mass produced carbon steel products such as kitchen knives.
C: Jump forward to a more modern steel production method.
If you want to mass produce industrial era quality steel, you need to do what we do in more modern steel production. 1st begin with crucible steel as described above, but use open crucibles with slag vents that you can hot blast with oxygen until all of the impurities (including the carbon) are removed. This will create a very soft but pure iron. Then in the final stage you add your charcoal to the crucible and seal it up to reintroduce the carbon in the final stage of smelting. This would yield steel that is going to be of a higher quality than the early industrial revolution because you can so much more precisely control for your final carbon content, and it can be made using very little charcoal relying mostly on burning oil.
Another Jump forward solution is to use petcoke as described in John's answer, but this is arguably a harder leap forward since the oil refineries needed to make the stuff are comparatively more complex and difficult to make without an already existing industrial age framework to support its manufacture.