This can be done using Response.Redirect()
:
Response.Redirect(String.Format("{0}?querystring=value", Request.CurrentExecutionFilePath));
However, I do not think it is possible to associate a query string with a URL without reloading the page again.
The query string in the url is not like an anchor. It may have an effects server side and is classified as a different URL from one without a query string. Therefore, it is not possible to bind a query string without reloading the page.
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