How to move setting field up a row on general page?

Use http://codex.wordpress.org/Settings_API to add new setting to existed group “general”:

add_action( 'admin_init', 'register_my_setting' );
function register_my_setting()
{
    add_settings_field('foo', 'Foo settings', 'foo_function', 'general', 'default', array('label_for' => 'foo'));
    register_setting('general', 'foo', 'foo value');
}
function foo_function()
{
    echo '<input name="foo" id="foo" value="" class="regular-text ltr">';
}

You must modify function to validate input and to show saved value.