I recently bought an 05 Ranger Fx4 Level ll and I'm wondering what the biggest tire size I can fit, It's on stock suspension with no sort of lift. The current size of the tires is LT235/75R15, I would like to keep the stock Alcoa rims.

 

Welcome to the forum

30.1" was the largest diameter STOCK tires on 2005 Ranger 4x4s, they were 10" wide
Your current tires are 28.9"

265/75R15 are 30.6" so a safe bet

31/10.5-R15 are of course 31" diameter and 10.5 wide and shouldn't rub, but it would be close, the problem is....... its NOT a new truck so suspensions sag a bit, and after 10+ years every Ranger will be slightly different

The rear tires are never an issue, just the front tires, and turning is where you can get the rubbing

 

If I was to lift it, would the 4.0l be able to turn 285/75R16s??

 

You need to post Diameters, 285/75R16 is 32.8" diameter, yes you would need a 3" lift

Any engine can run that size, the problem is the Ratio change because of the larger diameter
Truck will seem sluggish "off the line"

FX4 L2 should have 4.10 ratio axles
33" tires would knock that down to 3.60 actual ratio
To get it back to what it is now you would need to change front and rear axle to 4.56 Ratio

Or just live with the 3.60 ratio, which is not "bad" just won't feel as "peppy"

Brakes are what suffer the most with larger HEAVY tires, takes a bit more to stop big tires from spinning, so you will be replacing pads more often.
On the plus side you won't need ABS, lol, won't be locking up 33"s, well maybe on snow or ice