Easiest way to find out is to stick a clamp meter on it. If you don't have one, as usual, I can offer to loan you one and you can decline the offer. ;)
It also depends on what timescale you want to look at. As an inductive rather than resistive load, the current can have quite wild transients, but for average current, 3 to 10 A would be typical for a pre-engaged starter, and a clamp meter would be able to provide the average current no worries.
If you do want to know in more detail, and inductive probe and a storage oscilloscope and a good deal of calculation would be needed. A short loan of the equipment is possible.... ;)