If you want to allow this behaviour you need to disable rules on the settings screen. By default "normal" chess rules apply to the analysis board.
BUG: Chess.com mobile Analysis Board won't allow Rook to castle through a checked square

I probably am misunderstanding the question, but normal chess rules should allow a rook to travel from, through, and to squares under attack (i.e., checked squares), just not the king.

it is this game that I was analyzing. As you can see, as a result of an upcoming trade, the queen will be checking the rook square..
http://www.chess.com/echess/game.html?id=23438329
in the analysis board on my phone, it won't allow me to castle at that point. in the analyzer on the website, it will..
Mobile won't do it, but the site will