var texto= "//portal.sidiv.registrocivil.cl/docstatus?RUN=123456-4&type=CEDULA&serial=108538812&mrz=108538898884123132412311";
$("#probar").html(texto.match(/docstatus?(.*?)&type/));

<div id="probar"></div>

RUN=123456-4

var texto= "//portal.sidiv.registrocivil.cl/docstatus?RUN=123456-4&type=CEDULA&serial=108538812&mrz=108538898884123132412311";

var sign = texto.indexOf("?") + 1;
var and = texto.indexOf("&type");

$("#probar").html(texto.substring(sign,and));