Under the Vienna Convention, can a country waive its diplomat's immunity?

Yes. Under Article 32 of the Vienna Convention on Diplomatic Relations, the country sending a diplomat can expressly waive that diplomat's immunity from the receiving country's jurisdiction.

The treaty assigns this power to the sending state. UK Crown Prosecution Service guidance confirms the distinction: a diplomat cannot personally waive their own immunity, and a waiver must come from the sending state.

The scope of the waiver matters. Article 32 specifies that waiving immunity for civil or administrative proceedings does not automatically waive immunity from enforcement of the resulting judgment. That requires a separate waiver.