Castling in Chess960

Is there a consistent way to tell the board that I want to castle when playing chess960 vs just moving the King?

I believe you just move the king onto the rook

if you mean a separate button then no

After castling, the rook and king's final positions are exactly the same as they would be in standard chess. Thus, after a-side castling (also called sometimes c-castling) the king is on c-file (c1 for White and c8 for Black) and the a-side Rook is on d-file (d1 for White and d8 for Black). This castling notated as O-O-O and known as queen-side castling in orthodox chess. After h-side castling (also called sometimes g-castling) the King is on g-file and the h-side Rook is on f-file. This move notated as O-O and known as king-side castling in orthodox chess. It is recommended that a player state "I am about to castle" before castling, to eliminate potential misunderstanding.

(WIkipedia Chess 960)