Lord Tyre issued the order for Kim Avis,55, to be detained at the end of a short hearing at the High Court in Edinburgh on Monday.
Mr Avis, of Inverness, was due to stand trial in the Scottish capital on five charges of rape and alleged child sex offences.
However, Mr Avis, who is also known as Kim Gordon, failed to appear when the case called on Monday morning.
Police in California are currently trying to trace Mr Avis after he disappeared from Monastery Beach in Carmel last month.
He was reported missing by his 17-year-old son who said his dad had gone for swimming. Officers from the Monterey County Sheriff’s Office called off the search after spending two days looking for Mr Avis.
Mr Avis had made a personal appearance in the dock when the case previously called for a procedural hearing at the High Court in Glasgow.
Legal papers lodged in court detailing the charges against the accused state his name as being Kim Vincent Avis. The papers also state he is also known as Kem (CORR) Vincent Avis.
He is facing a total of 24 charges for rape, attempted rape, sexual assaults, lewd and libidinous conduct, breach of the peace, threatening behaviour and malicious damage offences.
He is alleged to have abused a total of four women between January 1997 and May 2015 at locations in Inverness, Inverness-shire and the Scottish Borders.
Two of his alleged victims were aged 11 when the alleged abuse against them commenced.
Mr Avis, a busker, denies any wrong doing.
On Monday, defence advocate Lorenzo Alonzi told Lord Tyre that he had no explanation for his client’s non attendance in court.
Mr Alonzi said Mr Avis’s disappearance had attracted “some press attention” and that his solicitors had tried to contact him.
He added: “There’s been no sign of him and there’s been mention of him in the media. His agents have tried to contact him by sending him text messages. But there’s been no response from him.”
Prosecution lawyer Jane Farquharson QC asked Lord Tyre to issue a warrant for his arrest.
She added: “The current indictment against him will have to fall.”
Prosecutors will issue a new indictment against Mr Avis if he is found by US law enforcement individuals.
Lord Tyre agreed and issued the warrant.
It is unclear when the next hearing against Mr Avis will take place.