Iranians are hoarding gold as a safeguard against a collapsing local currency and soaring cost of living as the U.S. is poised to impose economic sanctions on Iran, pushing the metal’s price to records in Tehran.

On Tuesday just after midnight U.S. Eastern time, the Trump administration is set to bring back a first wave of restrictions that had been waived under the Iran nuclear deal, an Obama-era agreement that gave Iran sanctions relief in exchange for curbs on its nuclear program.

President...