The lawsuit seeks unspecified damages over Spacey's alleged "explicit sexual behaviour and lewd and lascivious conduct" at The Club Car restaurant.
It states Spacey bought the man, then 18, alcoholic drinks and groped his genitals without his consent.
Prosecutors last year filed a related criminal case against Spacey - who denies the man's claims.
The Nantucket island allegations were first raised in 2017 by former television journalist Heather Unruh, who told reporters Spacey groped her teenage son.
This week's civil lawsuit, filed on Wednesday at Nantucket Superior Court in Massachusetts, states Spacey had bought him several rounds of beer and whiskey and said at one point, "Let's get drunk".
As they stood next to a piano, Spacey groped him, he told investigators.
Mobile phone 'missing'
The civil suit adds to an eventful month in the case.
Spacey's lawyers have accused Unruh's son of deleting text messages that would support the actor's defence.
In January, the judge overseeing his criminal case ordered Spacey's accuser to provide his mobile phone to the defence.
But the man's attorney, Mitchell Garabedian, later told the court the accuser cannot find the phone.
The judge has ordered Unruh, Mr Garabedian and the accuser to attend a hearing on 8 July if it cannot be found.
The case against Spacey is one of multiple allegations of sexual misconduct he is facing as part of Hollywood's #MeToo scandal.
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