Is there a way to link to a specific paragraph on a page without anchors?

You can only link to named anchors or elements with ids. If the target page has neither you are out of luck.

As of 2020, there is a draft by WICG for Text Fragments, and now you can link to text on a page as if you were searching for it by adding the following to the hash

#:~:text=<Text To Link to>

Working example on Chrome Version 81.0.4044.138:

Click on this link Should reload the page and highlight the link's text

I just noticed, that you want this on external source. If there are ids, you can use this: http://jsfiddle.net/LCgge/