Surely. You can use our browser extensions that will enable right click downloads to put.io on any page:
After installing, all you have to do is right clicking on any download link and selecting Download with put.io from the menu. Well, that technically makes two clicks.
We used to have a Safari extension too, but it won't work for Safari 12 and later because Apple doesn't accept .safariextz-style extensions anymore. Here's the related Apple announcement.
You can use following bookmark to fetch magnet links. Just add it to your bookmarks on Safari. Then you will be able to click that bookmark on the page you have magnet links and put.io will fetch it.
javascript:var%20magnetLinks%20=%20/(magnet:\?[^\s\"]*)/gmi.exec(document.body.innerHTML),win=(function(){window.open('https://put.io/default/magnet?url='+magnetLinks[0],'_blank');win.close();})();