Like a straight wire with resistance.
You will need to use the DC current value to determine where on the hysteresis loop you are operating, and then from the slope of the B-H curve at that point you can calculate the "inductance". I put the word inductance in quotes because when you are operating an iron core inductor near (or into) saturation, the inductor operation becomes non-linear and the concept of inductance is no longer appropriate. If the ripple current is nearly as large as the DC component, then one could say that the inductance is not constant. It's as though it varies from a small value when the operating point is well into saturation as the ripple current reaches its maximum, to a larger value when the operating point comes out of saturation and the ripple current reaches its minimum. You could use the average value of the "inductance" in calculations for a first try at analyzing the inductor. The usual methods of analyzing a circuit where linearity applies can no longer be used to give accurate results. You would have to simulate in Spice. Then you don't even specify "inductance"; you use a non-linear inductor model and specify its physical parameters.
A certain amount of trial and error might work best for you. Use the dimensions of the core and the known B-H curve for silicon steel to calculate the flux density in the core for your desired DC current. Pick a number of turns so that the DC current plus the expected maximum ripple current won't push the core too far into saturation. If the size wire you have to use to get that many turns on the core is too small, then the operating current may cause it to overheat, and you will need a bigger core. If the wire isn't going to overheat, then see if you get enough ripple reduction in actual operation. If not, then, again, you will need a bigger core. And, of course, the air gap will greatly affect all of this. It's not easy, especially when you're trying to use a core you already have on hand, instead of selecting one that calculations show will meet your requirements.