How to position custom dashboard widgets on side column

You’re right – it doesn’t. Neither does the wp_add_dashboard_widget function. So just use the generic add_meta_box and indicate dashboard and placement:

add_action( 'wp_dashboard_setup', 'my_dashboard_setup_function' );
function my_dashboard_setup_function() {
    add_meta_box( 'my_dashboard_widget', 'My Widget Name', 'my_dashboard_widget_function', 'dashboard', 'side', 'high' );
}
function my_dashboard_widget_function() {
    // widget content goes here
}