From actual birch sap, or from flavoring in a jar?
AFAIK, the actual birch sap has to be tapped from Betula lenta "cherry birch" (NOT white birch or paper birch--only cherry birch has the right wintergreen-y taste) trees in early spring, then boiled down like maple syrup, except you have to boil it 100:1 instead of 40:1. Then you'd just mix that with fizzy water and red food coloring to taste.
It can be made with extract, obviously, but danged if I can find a source for real birch extract. Even the internet is failing me...
Check your beer and wine supply stores. The one my DH goes to has all the flavorings to make root beer and birch and others.I remember seeing them there and thinking on making some.