URL Query String - Phone Number
It depends what you mean by "all records", but the custom search called full-text search (under Search - Custom Searches) can be made to run via url like so:

https://dmaster.demo.civicrm.org/civicrm/contact/search/custom?csid=15&amp;text=894-1515&amp;table=Contact&amp;force=1&amp;reset=1

That will bring up the contact with phone 894-1515.

If you want to include activities and such, then leave out the "table=Contact" part.