As described here, there is an API method for doing that in the YouTube Data API.
The documentation describes a method of forming an XML text format that automatically adds a video to your Watch Later playlist.
It will not work for you out of the box but with some moderate programming experience you (or someone else) should be able to make an application using this (a Chrome extension maybe).
The request would look like this:
POST https://gdata.youtube.com/feeds/api/users/default/watch_later HTTP/1.1 Host: gdata.youtube.com Content-Type: application/atom+xml Content-Length: [[CONTENT_LENGTH]] Authorization: Bearer [[ACCESS_TOKEN]] GData-Version: 2 X-GData-Key: key=[[DEVELOPER_KEY]] <?xml version="1.0" encoding="UTF-8"?> <entry xmlns="http://www.w3.org/2005/Atom" xmlns:yt="http://gdata.youtube.com/schemas/2007"> <id>[[VIDEO_ID]]</id> <yt:position>1</yt:position> </entry>