The callback is already passed arguments but crazily the codex doesn’t document them. However it does give you an example and the first two lines are:
function mytheme_comment($comment, $args, $depth) {
$GLOBALS['comment'] = $comment;
which matches the equivalent functions in the bundled styles. Once you’ve set the comment object passed as the global as in that example then you’re then free to use get_comment_ID() as usual.
If you didn’t want to set the global then
$my_comment_ID = apply_filters( 'get_comment_ID', $comment->comment_ID );
is equivalent, but it’s probably safer to go through get_comment_ID().