Yes they can. One way is through infected milk which is why milk is commonly pastuerized today. I have family in Ireland who are cattle farmers and the cattle are regularly checked for this illness since it is quite dangerous.Smallpox is another disease that may have been a mutation of an earlier bovine disease, cowpox. Humans can also get anthrax from farm animals and also contract Brucellosis.These types of illness are called zoonotic.