Yes it will. You have 1/2" wider rim which equalls 12.7mm or 6.35mm on each side of center. To have the outer lip be in the same place, you will need to go higher by 6.35mm in offset. (12mm + 6.35mm =18.35mm offset) So round it to +18mm or +19mm <---safer.
This applies ONLY as to where the lip will sit, if you are using the same size tire, it will stretch the tire a bit away from the edge with a wider rim. If your tire is NOT stretched now, you would be able to keep the same offset (+12mm) and the tire will sit in the same spot, but be a bit more stretched, and the rim lip will move "out" 6.35mm.
It all depends on your tire choice. What size are you using, and how "stretched" does it look? Can you post a pic?