The year 2371.
It depends which "Voyager" you mean. If you're talking about the USS Voyager, then it happened in 2371. If on the other hand you mean the Voyager 6 probe (which later became V'Ger), then there's no specific date known beyond the late 20th century.
For what it's worth, the Star Trek Chronology gives its launch date as 1999.Memory Alpha, the free Star Trek encyclopedia, has an answer to this question.
Please consult the Memory Alpha article "USS Voyager" for information.