The detection of elementary carriers in transport phenomena is one of the most important keys to understand nontrivial properties of strongly correlated quantum matter. Here, we propose a method to identify the tunneling current carrier in strongly interacting fermions from nonequilibrium noise in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover. The noise-to-current ratio, the Fano factor, can be a crucial probe for the current carrier. Bringing strongly correlated fermions into contact with a dilute reservoir produces a tunneling current in between. The associated Fano factor increases from one to two as the interaction becomes stronger, reflecting the fact that the dominant conduction channel changes from the quasiparticle tunneling to the pair tunneling.