River Birch are very susceptable to Chlorosis, a Ph induced nutrient deficiency.
Their is no ‘cure’, as the problem is the soil itself. You can however,relieve the symptoms for a year or two by applying soil acidifiers like iron sulfate, aluminum sulfate or any of the other products available to correct this condition.
A soil test may be a good place to start, in order to determine just how far off your soil is, and how much adjusting is needed (a ph in the neighborhood of 6.5 is ideal).
Whatever product you use be sure to read and follow label rates and directions.
Eliminating turf under the tree canopy (as far as the drip line)and appling a thin (3″ max. depth) layer of shredded bark mulch is also helpful.
Lastly, remember that it is a River Birch, i.e., a bottomland plant, and will do best on moist soil (this does not mean compacted clay) this tree needs frequent watering in our normal hot dry summers.