He told the party’s annual conference in Bournemouth that it was “shocking” that ministers had “appealed to the personal financial interests of an American president to curry favour”.
In April, the government said that it was up to the R&A to decide the hosts of the tournament after reports that President Trump had spoken to Sir Keir Starmer about the matter.
Turnberry has hosted the Open Championship on four occasions, with the last time being in 2009.
In July the government announced that a new Ethics and Integrity Commission would be established “to drive up standards in public life”.
Miller said ministers “must show that this commission can truly protect our values from foreign corruption” and called on the government “to refer its own lobbying over Turnberry as the first case for investigation”.
He accused Labour of being “willing to do almost anything to appease Donald Trump”.
When the claims about Sir Keir and President Trump having discussed the tournament first surfaced, a spokesman for the prime minister didn’t deny the conversations had taken place but said any contact ministers had with sporting bodies was “part of the business of government” and not hosting decisions.
They added: “Obviously the government is in regular contact with sporting bodies on tournaments in the usual way but not beyond that.”
The government has said the new ethics commission would “have an ambitious remit to uphold the highest ethical standards across the public sector”.
The government has been approached for comment.
