One of the uses of the word "to" is to show how people or things are related. He's the assistant to the president. = he and the president are related. How? He's the assistant. He's related to me. He's been a good friend to me. A is of senior rank to B. = A and B are related. In what way? A is the senior. If someone is your senior, he has a higher standing or rank than you. To take charge is to be responsible in managing or looking after someone/something. A is of senior rank to B so A takes charge. = A is the senior so he gets to supervise and not B.

A simplified form would be "A is greater than B, therefore A is the leader". So, in this instance, "to" is performing the same function as "than". It is a comparison. Another way of expressing it would be, "A is of more senior rank with regards to B". So "to" equates to "with regards to". Finally, "rank to" is not a specific expression.

I think "rank" is originally a military expression. Informally, it has come to refer to levels of authority in any hierarchical organization. In a military context, we might say "He has the rank of colonel," or "in the Navy, a captain outranks a commander." In a corporation, someone might say "I didn't argue with her; she's a vice-president and outranks me." Referring to the hierarchy of the Roman Catholic Church, someone might say "only six cardinals held the rank of Cardinal Bishop." To "take charge" can mean "to give the orders." One might imagine a conversation: "Thank you, Constable Jones. You've done good work here. But Detective Inspector Lynley has just arrived from Scotland Yard and he will be taking charge of this case now."