Noyac is right, you will definitely need better than average step 1 and 2 scores, but I'm sure you already knew that. I would definitely recommend completing at least 2 anesthesia rotations as a visiting student at a place you would like to end up matching and obtain as many LORs as possible from that place. I ended up doing my 2 anesthesia rotations at UTHSCSA, one in general OR anesthesia and the other in OB anesthesia. If possible, try to do them towards the end of the academic year (b/w march-may) because most US med students are done with their elective rotations around that time and you'll be the only student, or maybe one of a few students in that rotations and that will give you the opportunity to shine and do a lot of procedures.
If you are able to do that, keep in mind that it could be a double-edged sword and backfire, but as long as you work your tail off, request an extra call to get more hands on experience, always be the first to volunteer for procedures and just show them that you are extremely interested, you will score yourself some very strong LORs, which is also extremely important.
Finally, as far as board scores go, who knows, but I can tell you my credentials and you can go from there. I scored a 219 on my step 1, 242 on step 2, had, what I thought were some killer LORs (make sure you get one from the chairman and make sure to meet with him and the program director!!!) and I ended up with 18 interviews, ranked 16 of them and matched into my 3rd pick. The bottom line is that you have to be very proactive about this and if you sit back, do a rotation in anesthesia at one of the "cheap" hospitals that sponsor St. Matthews (just like the somewhat "cheap" hospitals that Ross University has, where I graduated from), you would have put yourself at a huge disadvantage, because most IMGs, at least USIMGs that match have done what I did, with good results. Good luck and keep your head up and be ready to work your tail off if you want to match!
