Can si joint inflammation cause calf nerve pain?

Depends. If you already have sciatica and it involves your si joint too, this nerve goes all the way down to the foot, and can affect any part of the nerve that shoots off from it. To double check, you need to see a PCP/Dr. to get this checked out and see for sure. A sports medicine, or osteopathic (DO) physician are well trained to see this, as are neurologist or orthopedist. Start with your PCP first!