In these cases, I do one of three things:
1. If the anchor rod projects less than 1/2" above the base plate, full pen weld an extension onto the short anchor rod.
2. Otherwise, have them fab a 1/4" thick plate with a 1/16" oversize hole centered. Then they can place this over the rod, and fillet weld the rod to this new plate. Then they fillet weld the new plate to the base plate. This works well with the oversize holes used in the base plates, as directly welding the rod to the base plate is basically nearly impossible. Of course, you would need to check plate stresses in this case. Also, if you have significant shear loads transfering through the anchor rods, this might not be good, as the weld would be sharing loads with the bolted rods.
3. If the rod is below the top of the base plate, such that they can not full pen weld, then the last option is to drill a new hole through the base plate and epoxy dowel new anchor rod into the foundation. Size of rod might need to be adjusted based on allowable strength of the epoxy connection.
Hope this helps some.
Andrew