Try to ignore some of what was written above...some people are just misinformed.
People like TIG because it is pretty. You are welding an exhaust (that no one will see) so we really don't care how pretty it is.
You will be able to use your MIG just fine. I assume it is a 110V welder that runs .030" wire. Go to your nearest welding supply company and tell them you are wanting to weld some stainless exhaust pipe and you need a suitable wire for the job. More than likely they will have small (5lb) spools of .025" or .030" 308L (for SS to SS) and 309L (SS to carbon steel) welding wire. Use that. You will also need a different shielding gas for this job (98%Argon 2% Oxygen would be the most preferred). The wire will be ~$8 per pound and the gas will be not too bad for a small bottle (5-10 cubic feet). Once you have what you need you need to just play with the machine until you get the desired weld bead (nice and flat with no overlapping edges and enough penetration).
If you have any more questions feel free to ask. I am a new Subaru owner but not new to welding (B.S. in Welding Engineering in fact).
Hope that helps!