Yes — Scottish Borders says you can report fly tipping by phone on 0300 100 1800 or through its fly tipping online form. The published guidance doesn’t say whether anonymous reporting is allowed for fly tipping, so I can’t confirm that from the available council information.
If you want to stay anonymous, the closest confirmed option in the council’s records is its fraud reporting service, which does allow anonymous reports — but that’s for fraud, not fly tipping.