Bald Eagles generally don't eat rodents or other birds, they're a type of fish eagle and thus... eat fish.
That said, they are decently sized. On average they weight in between 6 to 14 lbs (2.7 to 6.3 kg), have a body length between 28 to 38 inches (71 to 97 cm) and have a wingspan of 80 inches (203 cm).
The reason the cat has to be concerned is that the Bald Eagle's talons can be quite long and sharp, and its feathers actually offer it a degree of protection against the cat's claws, plus it's big enough that the cat would have trouble going for a neck break. In general predators of the same size won't fight each other unless backed into a corner or protecting young, as neither side generally has much to gain over the fight and injuries from it could end them even if they win. In fact, that cat and eagle have little to fight over, as they don't actually compete for the same prey.