Googling led me to this page where the author had the same problem, and they found a solution in Safari Bookmarks Extractor. I can't test that it still works with version changes in both, but it probably does. Once you have your extracted bookmarks, you just use Manage Bookmarks -> File -> Import -> From File.
I need to correct you here: on Android devices, the ability to install applications that aren't from the Google Play store is available regardless if the device has been rooted or not. There's an option available that allows you to do so.