While I understand that it is not customary or typical to acquire website links though the Twitter platform, it is quite possible - however probable to expect.

What methods or techniques might be used to encourage a website link? Is there anything?

Simply searching for a type of account tagline, like "Editor at some site"? Even then, are they apt to make the transfer, from Twitter to posting a link on their own site page? Seems the driving reason/motivation behind it would have to be a strong one.