Arpaio earlier this year, said that because the former sheriff had a choice of either accepting Mr. Trump's pardon or continuing to fight his conviction in an appeals court.
Arpaio had been convicted of criminal contempt in July for violating a federal judge's order to stop detaining citizens based only on a suspicion they were in the country illegally.
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Bolton presided over a five-day trial; she found Arpaio guilty on July 31 and ordered him to be sentenced on October 5 - but President Trump intervened with a pardon in late August. "The pardon undoubtedly spared (the) defendant from any punishment that might otherwise have been imposed".
She continued: "To vacate all rulings in this case would run afoul of this important distinction". That is, what interests me is how little her reasoning depends on the rather extraordinary background of this case-background so extraordinary that I, like some others, thought there was a conceivable argument for the invalidity of the pardon itself. Justice Department lawyers filed a brief with the court arguing that "the court should vacate all orders and dismiss the case as moot".
A presidential pardon "does not erase a judgment of conviction, or its underlying legal and factual findings", Bolton wrote.
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In her ruling, Bolton wrote that the objective of a pardon was not to wipe a defendant's record clean or "blot out guilt", but to prevent further punishment for the crime and restore the his or her civil rights.
He gained popularity for his hard-line views against undocumented immigrants, but rising court costs in the 2007 lawsuit lost him favor with Maricopa County taxpayers.
For the former sheriff's opponents, the ruling is a small victory in the face of a heartbreaking deus ex machina pardon from Arpaio's pal in the White House, after years of legal battles and last year's campaign, which forced the sheriff from an office he had held for decades.
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Arpaio's attorneys have appealed the judge's ruling to the 9th US Circuit Court of Appeals. Attorney General Jeff Sessions, testifying to the Senate Judiciary Committee this week, said he was not sure whether Trump had the power to pardon himself, should the matter arise.