Apple just unified the clipboard with your iPhone if you’re on iOS 10 and macOS Sierra, anything you copy on one is now accessible on the other. Even with that added functionality though the experience leaves a bit to be desired. Pastebot by Tapbots, who brought us Tweetbot seeks to fill this gap.
Pastebot is currently available as a public beta and can be installed here, but before doing so head on over to their help page to make sure you’re all set regarding system requirements. It’s also a good idea to read up on the installation process as there’s a tiny bit of manual set up you’ll need to do to get around application sandboxing.