Question

Is it possible? Or is there any other way to do it without xml-rpc?

Answer 1

Yes, it is possible, but you have to write your own xml-rpc method.

For example:

add_filter( 'xmlrpc_methods', 'my_add_xmlrpc_methods' );

//this function adds new xml-rpc method
//my.search_posts - name of xml-rpc method
//search_posts_by_custom_field - name of the function that should proccess my.search_posts method call
function my_add_xmlrpc_methods( $methods ) {
    $methods['my.search_posts'] = 'search_posts_by_custom_field';
    return $methods;
}

//this function actually search posts
function search_posts_by_custom_field($args) {
    //authenticate user
    //run search DB query
    //return results
}