A method for making downhole electromagnetic logging while drilling measurements includes rotating an electromagnetic logging while drilling tool in a subterranean wellbore. The logging tool includes first and second transmitters, each of which includes a tilted antenna, and a receiver axially spaced apart from one another. Electromagnetic voltage measurements are made at the receiver while the tilted transmitting antenna in the first transmitter fires during tool rotation. The electromagnetic voltage measurements are mathematically rotated through at least the arbitrary angle to obtain rotated measurements, selected ratios of which are processing to compute gain compensated measurement quantities.