A better choice could be to display the board using an array of type char. And you can always convert the characters to integers, or use board's index if you need to use them for calculations(which I doubt you will have to).
char board[9] {
'1', '2', '3', '4', '5', '6', '7', '8', '9'
};
if you need access to those integer values just use the board's index+1.
You can use this:
cin >> movePosition;
to accept user's input. and when you need to edit the board just use:
board[movePosition-1] = 'X';
or
board[movePosition-1] = 'O';
This will now work as the array is of type char.