Create a bookmark to a site in the dock
Yes it is. If Google Chrome is your default browser.

Procedure


Go to Trello.com in Chrome
Drag the text in the URL field to the desktop. This will create a document that ends in .webloc. EG "Trello.webloc"
Drag that icon into the right side of the dock (it's a document and has to be to the right of the divider bar)


I had forgotten that you could drag the bookmark out of the URL bar directly into the dock. Do it that way if it suits you, either works.

Now when you click on that icon trello.com (or any .webloc document) will open in your default browser.

(This works in Safari and I don't have Chrome handy on this Mac to test. I am assuming that Chrome for Mac behaves the same as Safari in this respect)